(2021) Global conservative solution for the periodic dispersive Hunter–Saxton equation. Nonlinear Analysis: Real World Applications 59, 103248. Crossref

(2021) Integrability structures of the generalized Hunter–Saxton equation. Analysis and Mathematical Physics 11:2. Crossref

(2021) Global asymptotic stabilization of the Hunter-Saxton control system. European Journal of Control 127. Crossref

(2021) Nanomanipulation of elliptic and cubic nanoparticles with consideration of the impact theories. Applied Mathematical Modelling 90, 101-113. Crossref

(2021) Can we run to infinity? The diameter of the diffeomorphism group with respect to right-invariant Sobolev metrics. Calculus of Variations and Partial Differential Equations 60:1. Crossref

(2021) Periodic peakons to a generalized μ -Camassa–Holm–Novikov equation. Applicable Analysis, 1-11. Crossref

(2021) Numerical conservative solutions of the Hunter–Saxton equation. BIT Numerical Mathematics 37. Crossref

(2021) Weakly nonlinear interactions of collective oscillations in a correlated degenerate fluid. Waves in Random and Complex Media 8, 1-23. Crossref

(2021) The Hunter–Saxton equation with noise. Journal of Differential Equations 270, 725-786. Crossref

(2020) The r-Hunter–Saxton equation, smooth and singular solutions and their approximation. Nonlinearity 33:12, 7016-7039. Crossref

(2020) Solutions of Second-Order PDEs with First-Order Quotients. Lobachevskii Journal of Mathematics 41:12, 2491-2509. Crossref

(2020) Berry phases in the reconstructed KdV equation. Chaos: An Interdisciplinary Journal of Nonlinear Science 30:11, 113114. Crossref

(2020) Numerical Investigation Based on Laguerre Wavelet for Solving the Hunter Saxton Equation. International Journal of Applied and Computational Mathematics 6:5. Crossref

(2020) Singularity and existence for a multidimensional variational wave equation arising from nematic liquid crystals. Journal of Mathematical Analysis and Applications 487:2, 124026. Crossref

(2020) Orbital Bifurcations and Shoaling of Cnoidal Waves. Journal of Mathematical Fluid Mechanics 22:2. Crossref

(2020) Multisoliton solutions of the Degasperis–Procesi equation and its shortwave limit: Darboux transformation approach. Theoretical and Mathematical Physics 203:2, 608-620. Crossref

(2020) Fractional Sobolev metrics on spaces of immersions. Calculus of Variations and Partial Differential Equations 59:2. Crossref

(2020) Semi-invariant Riemannian metrics in hydrodynamics. Calculus of Variations and Partial Differential Equations 59:2. Crossref

(2020) Parametric solutions of the generalized short pulse equations. Journal of Physics A: Mathematical and Theoretical 53:10, 105202. Crossref

(2020) Vanishing Distance Phenomena and the Geometric Approach to SQG. Archive for Rational Mechanics and Analysis 235:3, 1445-1466. Crossref

(2020) Generalized Compressible Flows and Solutions of the $$H(\mathrm {div})$$ Geodesic Problem. Archive for Rational Mechanics and Analysis 235:3, 1707-1762. Crossref

(2020) Global existence for the periodic dispersive Hunter–Saxton equation. Monatshefte für Mathematik 191:2, 267-278. Crossref

(2019) Hamiltonian operators and related differential-algebraic Balinsky-Novikov, Riemann and Leibniz type structures on nonassociative noncommutative algebras. Proceedings of the International Geometry Center 12:4. Crossref

(2019) Existence and Uniqueness of Solutions for a Quasilinear KdV Equation with Degenerate Dispersion. Communications on Pure and Applied Mathematics 72:11, 2449-2484. Crossref

(2019) Analytical Techniques for Solving Nonlinear Partial Differential Equations. Synthesis Lectures on Mathematics and Statistics 11:3, 1-165. Crossref

(2019) Analytical Cartesian solutions of the multi-component Camassa-Holm equations. Journal of Nonlinear Mathematical Physics 26:2, 255-272. Crossref

(2019) A Lipschitz metric for the Hunter–Saxton equation. Communications in Partial Differential Equations 44:4, 309-334. Crossref

(2019) On the stationary solutions and inviscid limit for the generalized Proudman–Johnson equation with O(1) forcing. Journal of Mathematical Analysis and Applications 472:1, 842-863. Crossref

(2019) Local well-posedness and blow-up phenomena of the generalized short pulse equation. Journal of Mathematical Physics 60:4, 041505. Crossref

(2019) Stability and convergence of a conservative finite difference scheme for the modified Hunter–Saxton equation. BIT Numerical Mathematics 59:1, 213-241. Crossref

(2019) Unique Solvability of a Coupling Problem for Entire Functions. Constructive Approximation 49:1, 123-148. Crossref

(2019) A Method of Solving Compressible Navier Stokes Equations in Cylindrical Coordinates Using Geometric Algebra. Mathematics 7:2, 126. Crossref

(2019) Investigating the impact models for nanoparticles manipulation based on atomic force microscope (according to contact mechanics). Powder Technology 344, 17-26. Crossref

2019. Lectures on Geometry of Monge–Ampère Equations with Maple. Nonlinear PDEs, Their Geometry, and Applications, 53-94. Crossref

(2018) Idea of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs. Applied Mathematics and Computation 339, 158-171. Crossref

(2018) On the Cauchy problem for a nonlinear variational wave equation with degenerate initial data. Nonlinear Analysis 176, 192-208. Crossref

(2018) Well-posedness and peakons for a higher-order $\mu$ -Camassa–Holm equation. Nonlinear Analysis 175, 210-236. Crossref

(2018) The Hunter-Saxton Equation: A Numerical Approach Using Collocation Method. Numerical Methods for Partial Differential Equations 34:5, 1637-1644. Crossref

(2018) Non-uniform dependence of the data-to-solution map for the Hunter–Saxton equation in Besov spaces. Journal of Evolution Equations 18:3, 1173-1187. Crossref

(2018) Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system. Journal of Hyperbolic Differential Equations 15:03, 559-597. Crossref

(2018) Degenerate form of a three-component Degasperis–Procesi equation. Journal of Mathematical Analysis and Applications 464:2, 1082-1088. Crossref

(2018) The existence of solitary wave solutions of delayed Camassa–Holm equation via a geometric approach. Journal of Functional Analysis 275:4, 988-1007. Crossref

(2018) The existence of the single peaked traveling waves to the -Novikov equation. Applicable Analysis 97:9, 1540-1548. Crossref

(2018) A Synthetical Two-Component Model with Peakon Solutions: One More Bi-Hamiltonian Case. Zeitschrift für Naturforschung A 73:5, 425-430. Crossref

(2018) New variational and multisymplectic formulations of the Euler–Poincaré equation on the Virasoro–Bott group using the inverse map. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474:2213, 20180052. Crossref

(2018) The Mixed Kuper-Camassa-Holm-Hunter-Saxton Equations. Journal of Nonlinear Mathematical Physics 25:2, 179-187. Crossref

(2018) Global existence of weak solutions to dissipative transport equations with nonlocal velocity. Nonlinearity 31:4, 1484-1515. Crossref

(2018) The global attractor for a viscous weakly dissipative generalized two-component μ-Hunter-Saxton system. Acta Mathematica Scientia 38:2, 651-672. Crossref

(2018) Optimal solution and optimality condition of the Hunter-Saxton equation. Journal of Mathematical Physics 59:2, 021507. Crossref

(2018) Conservation Laws of The Generalized Riemann Equations. Journal of Nonlinear Mathematical Physics 25:1, 122-135. Crossref

2018. Models and Special Solutions of the Navier-Stokes Equations. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 729-780. Crossref

(2017) A convergent finite difference scheme for the variational heat equation. Zeitschrift für angewandte Mathematik und Physik 68:6. Crossref

(2017) Existence of smooth solutions to a one-dimensional nonlinear degenerate variational wave equation. Nonlinear Analysis 165, 80-101. Crossref

(2017) Generalizations of the short pulse equation. Letters in Mathematical Physics 81. Crossref

(2017) Well-posedness and large deviations for a class of SPDEs with Lévy noise. Journal of Differential Equations 263:9, 5216-5252. Crossref

(2017) Global existence and local well-posedness of the single-cycle pulse equation. Journal of Mathematical Physics 58:10, 101515. Crossref

(2017) Well-posedness and wave breaking of the degenerate Novikov equation. Journal of Differential Equations 263:8, 4634-4657. Crossref

(2017) Multisoliton solutions of the two-component Camassa–Holm system and their reductions. Journal of Physics A: Mathematical and Theoretical 50:34, 345202. Crossref

(2017) Geometric numerical integrators for Hunter–Saxton-like equations. Japan Journal of Industrial and Applied Mathematics 34:2, 441-472. Crossref

(2017) Blow-up phenomena and travelling wave solutions to the periodic integrable dispersive Hunter-Saxton equation. Discrete and Continuous Dynamical Systems 37:12, 6471-6485. Crossref

(2017) Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation. Communications in Nonlinear Science and Numerical Simulation 48, 270-277. Crossref

(2017) Local discontinuous Galerkin schemes for a nonlinear variational wave equation modelling liquid crystals. Journal of Computational and Applied Mathematics 317, 478-499. Crossref

(2017) An Efficient Numerical Solution of Nonlinear Hunter–Saxton Equation. Communications in Theoretical Physics 67:5, 483. Crossref

(2017) Peakompactons: Peaked compact nonlinear waves. International Journal of Modern Physics B 31:10, 1742008. Crossref

(2017) Global solutions to a nonlinear wave system arising from cholesteric liquid crystals. Journal of Hyperbolic Differential Equations 14:01, 27-71. Crossref

(2017) G -Strands on symmetric spaces. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473:2199, 20160795. Crossref

(2017) Fractional Hunter-Saxton equation involving partial operators with bi-order in Riemann-Liouville and Liouville-Caputo sense. The European Physical Journal Plus 132:2. Crossref

(2017) Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems. Journal of Nonlinear Mathematical Physics 24:1, 41-72. Crossref

2017. Numerical Experiments on a Nonlinear Wave Equation with Singular Solutions. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, 481-493. Crossref

(2017) Generic regularity and Lipschitz metric for the Hunter–Saxton type equations. Journal of Differential Equations 262:2, 1023-1063. Crossref

(2016) On Isospectral Deformations of an Inhomogeneous String. Communications in Mathematical Physics 348:3, 771-802. Crossref

(2016) Non-uniform dependence on initial data for the modified μ-Camassa–Holm equation. Journal of Differential Equations 261:11, 6099-6124. Crossref

(2016) On the Cauchy problem for a weakly dissipative generalized $$\mu $$ μ -Hunter-Saxton equation. Monatshefte für Mathematik 181:3, 715-744. Crossref

(2016) Global exact controllability and asympotic stabilization of the periodic two-component $\mu\rho$-Hunter-Saxton system. Discrete and Continuous Dynamical Systems - Series S 9:6, 2129-2148. Crossref

(2016) On the Cauchy problem of the modified Hunter-Saxton equation. Discrete and Continuous Dynamical Systems - Series S 9:6, 2047-2072. Crossref

(2016) Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons. Journal of Nonlinear Mathematical Physics 23:4, 563-572. Crossref

(2016) On a Lagrangian Reduction and a Deformation of Completely Integrable Systems. Journal of Nonlinear Science 26:5, 1133-1160. Crossref

(2016) Multi-soliton solution to the two-component Hunter–Saxton equation. Wave Motion 65, 17-28. Crossref

(2016) The tri-Hamiltonian dual system of supersymmetric two boson system. Physics Letters A 380:38, 3073-3080. Crossref

(2016) Multipeakons of a two-component modified Camassa–Holm equation and the relation with the finite Kac–van Moerbeke lattice. Advances in Mathematics 299, 1-35. Crossref

(2016) A semi-analytical solution of Hunter–Saxton equation. Optik 127:13, 5255-5258. Crossref

(2016) The inverse spectral problem for indefinite strings. Inventiones mathematicae 204:3, 939-977. Crossref

(2016) Well-posedness and the small time large deviations of the stochastic integrable equation governing short-waves in a long-wave model. Nonlinear Analysis: Real World Applications 29, 38-57. Crossref

(2016) Integrability and Solutions of the (2 + 1)-dimensional Hunter–Saxton Equation. Communications in Theoretical Physics 65:4, 397-404. Crossref

(2016) Relation between the Negative-Order Harry Dym Hierarchy and a Family of Backward Neumann Type Systems. Journal of the Physical Society of Japan 85:3, 034004. Crossref

(2016) Conservation laws and symmetries of Hunter–Saxton equation: revisited. Nonlinearity 29:3, 737-755. Crossref

(2016) Uniqueness of conservative solutions for nonlinear wave equations via characteristics. Bulletin of the Brazilian Mathematical Society, New Series 47:1, 157-169. Crossref

(2016) Energy conservative solutions to the system of full variational sine-Gordon equations in a unit sphere. Journal of Mathematical Physics 57:2, 021503. Crossref

(2016) Maximal dissipation in Hunter–Saxton equation for bounded energy initial data. Advances in Mathematics 290, 590-613. Crossref

2016. Models and Special Solutions of the Navier–Stokes Equations. Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, 1-52. Crossref

(2016) Analysis of time-fractional hunter-saxton equation: a model of neumatic liquid crystal. Open Physics 14:1, 145-149. Crossref

(2015) Well-posedness for the Cauchy problem of the modified Hunter-Saxton equation in the Besov spaces. Mathematical Methods in the Applied Sciences 38:17, 4061-4074. Crossref

(2015) On initial data problem for a periodic two-component μ -Hunter-Saxton system. Mathematical Methods in the Applied Sciences 38:17, 4249-4261. Crossref

(2015) Nonlocal symmetries and conservation laws of nonlocal Camassa-Holm type equations. Acta Mathematicae Applicatae Sinica, English Series 31:4, 909-920. Crossref

(2015) The Role of Inertia and Dissipation in the Dynamics of the Director for a Nematic Liquid Crystal Coupled with an Electric Field. Communications in Computational Physics 18:1, 147-166. Crossref

(2015) Conservative solutions to a one-dimensional nonlinear variational wave equation. Journal of Differential Equations 259:1, 172-200. Crossref

(2015) Wave breaking and global existence for a weakly dissipative generalized two-component <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>μ</mml:mi></mml:math>-Hunter–Saxton system. Nonlinear Analysis: Real World Applications 23, 61-77. Crossref

(2015) On initial data problem for a periodic 2-component $$\mu $$ μ -b system. Journal of Applied Mathematics and Computing 48:1-2, 553-571. Crossref

(2015) Longitudinal dust acoustic solitary waves in a strongly coupled complex (dusty) plasma. Journal of Plasma Physics 81:3. Crossref

(2015) Several Types of Similarity Solutions for the Hunter–Saxton Equation. Communications in Theoretical Physics 63:6, 675-681. Crossref

(2015) Wave-breaking phenomenon for a generalized spatially periodic Camassa-Holm system. Mathematical Methods in the Applied Sciences 38:7, 1405-1417. Crossref

(2015) ANALYTIC SOLUTIONS OF THE CAUCHY PROBLEM FOR THE GENERALIZED TWO-COMPONENT HUNTER-SAXTON SYSTEM. Honam Mathematical Journal 37:1, 99-112. Crossref

(2015) Existence and regularity of solutions in nonlinear wave equations. Discrete and Continuous Dynamical Systems 35:8, 3327-3342. Crossref

(2015) Conservative weak solutions of the periodic Cauchy problem for μ HS equation. Journal of Mathematical Physics 56:2, 021504. Crossref

(2015) Effects of Quadratic Singular Curves in Integrable Equations. Studies in Applied Mathematics 134:1, 24-61. Crossref

(2015) The Periodic Boundary Value Problem for the Weakly Dissipative $\mu$ -Hunter-Saxton Equation. Advances in Mathematical Physics 2015, 1-9. Crossref

(2015) Global estimates and blow-up criteria for the generalized Hunter-Saxton system. Discrete and Continuous Dynamical Systems - Series B 20:2, 641-673. Crossref

(2014) A note on the Cauchy problem of a modified Camassa-Holm equation with cubic nonlinearity. Discrete and Continuous Dynamical Systems 35:5, 2011-2039. Crossref

(2014) Collective dynamics in strongly coupled dusty plasma medium. Journal of Plasma Physics 80:6, 855-861. Crossref

(2014) Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy. Journal of Nonlinear Mathematical Physics 21:4, 473-508. Crossref

(2014) The spatially periodic Cauchy problem for a generalized two-component -Camassa–Holm system. Nonlinear Analysis: Real World Applications 19, 117-134. Crossref

(2014) A generalized nonisospectral Camassa–Holm equation and its multipeakon solutions. Advances in Mathematics 263, 154-177. Crossref

(2014) Overview of the Geometries of Shape Spaces and Diffeomorphism Groups. Journal of Mathematical Imaging and Vision 50:1-2, 60-97. Crossref

(2014) Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle. Journal of Geometric Mechanics 6:3, 335-372. Crossref

(2014) Exact propagating nonlinear singular disturbances in strongly coupled dusty plasmas. Physics of Plasmas 21:8, 083701. Crossref

(2014) Novikov Algebras and a Classification of Multicomponent Camassa-Holm Equations. Studies in Applied Mathematics 133:1, 84-117. Crossref

(2014) Notes on “Solitary wave solutions of the generalized two-component Hunter–Saxton system”. Nonlinear Analysis: Theory, Methods & Applications 103, 33-38. Crossref

(2014) Algebro-geometric solutions for the Hunter–Saxton hierarchy. Zeitschrift für angewandte Mathematik und Physik 65:3, 487-520. Crossref

(2014) Hölder continuity on <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>μ</mml:mi><mml:mtext>-</mml:mtext><mml:mi>b</mml:mi></mml:math> equation. Nonlinear Analysis: Theory, Methods & Applications 102, 30-35. Crossref

(2014) Associate symmetries: A novel procedure for finding contact symmetries. Communications in Nonlinear Science and Numerical Simulation 19:3, 431-441. Crossref

(2014) On the Cauchy problem of a weakly dissipative μ-Hunter–Saxton equation. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 31:2, 267-279. Crossref

(2014) Orbital Stability of Periodic Peakons to a Generalized μ-Camassa–Holm Equation. Archive for Rational Mechanics and Analysis 211:2, 593-617. Crossref

(2014) New Distributional Global Solutions for the Hunter-Saxton Equation. Abstract and Applied Analysis 2014, 1-9. Crossref

(2014) On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation. Advances in Mathematical Physics 2014, 1-6. Crossref

(2014) Bifurcation Analysis and Different Kinds of Exact Travelling Wave Solutions of a Generalized Two-Component Hunter-Saxton System. Advances in Mathematical Physics 2014, 1-10. Crossref

(2014) Well-posedness, wave breaking and peakons for a modified μ -Camassa–Holm equation. Journal of Functional Analysis 266:2, 433-477. Crossref

(2013) On the higher-order b-family equation and Euler equations on the circle. Discrete and Continuous Dynamical Systems 34:7, 3013-3024. Crossref

(2013) Conservative solutions to a system of asymptotic variational wave equations. Journal of Mathematical Analysis and Applications 408:2, 725-732. Crossref

(2013) Rational solutions from Padé approximants for the generalized Hunter-Saxton equation. Journal of Physics: Conference Series 474, 012006. Crossref

(2013) Non-uniform dependence on initial data for the μ − b equation. Zeitschrift für angewandte Mathematik und Physik 64:5, 1543-1554. Crossref

(2013) Solitary wave solutions of the generalized two-component Hunter–Saxton system. Nonlinear Analysis: Theory, Methods & Applications 89, 242-249. Crossref

(2013) Blow-up of Solutions to the Generalized Inviscid Proudman–Johnson Equation. Journal of Mathematical Fluid Mechanics 15:3, 493-523. Crossref

(2013) On the weakly dissipative Camassa–Holm, Degasperis–Procesi, and Novikov equations. Journal of Differential Equations 255:3, 441-448. Crossref

(2013) Coupled Camassa–Holm equations, -peakons and infinitely many conservation laws. Journal of Mathematical Analysis and Applications 403:1, 262-271. Crossref

(2013) Spheres, Kähler geometry and the Hunter–Saxton system. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469:2154, 20120726. Crossref

(2013) The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems. Reports on Mathematical Physics 71:3, 305-351. Crossref

(2013) Weak solutions to a nonlinear variational sine–Gordon equation. Journal of Mathematical Analysis and Applications 402:1, 1-11. Crossref

(2013) The Hunter-Saxton System and the Geodesics on a Pseudosphere. Communications in Partial Differential Equations 38:5, 860-881. Crossref

(2013) Stability of periodic peakons for the modified -Camassa–Holm equation. Physica D: Nonlinear Phenomena 250, 66-74. Crossref

(2013) Symmetry Analysis and Conservation Laws for the Hunter—Saxton Equation. Communications in Theoretical Physics 59:3, 335-348. Crossref

(2013) Geometry of Diffeomorphism Groups, Complete integrability and Geometric statistics. Geometric and Functional Analysis 23:1, 334-366. Crossref

(2013) Two supersymmetric hierarchies related to the super-HS spectral problem. Communications in Nonlinear Science and Numerical Simulation 18:2, 257-263. Crossref

(2013) Stability of the μ-Camassa–Holm Peakons. Journal of Nonlinear Science 23:1, 97-112. Crossref

(2013) On the model of the compressible hyperelastic rods and Euler equations on the circle. Journal of Differential Equations 254:2, 648-659. Crossref

(2013) Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation. Abstract and Applied Analysis 2013, 1-5. Crossref

(2013) Wave-Breaking Criterion for the Generalized Weakly Dissipative Periodic Two-Component Hunter-Saxton System. Journal of Applied Mathematics 2013, 1-10. Crossref

(2013) Blow up of Solutions and Traveling Waves to the Two-Component μ-Camassa–Holm System. International Mathematics Research Notices 2013:15, 3386-3419. Crossref

(2012) Global weak solutions for a periodic two-component μ-Hunter–Saxton system. Monatshefte für Mathematik 168:3-4, 503-521. Crossref

(2012) Global energy conservative solutions to a system of variational wave equations. Nonlinear Analysis: Theory, Methods & Applications 75:18, 6418-6432. Crossref

(2012) Global solutions to a class of nonlinear damped wave operator equations. Boundary Value Problems 2012:1. Crossref

(2012) Global Existence for the Generalized Two-Component Hunter–Saxton System. Journal of Mathematical Fluid Mechanics 14:3, 455-469. Crossref

(2012) Non-metric two-component Euler equations on the circle. Monatshefte für Mathematik 167:3-4, 449-459. Crossref

(2012) The modified Hunter–Saxton equation. Journal of Geometry and Physics 62:8, 1793-1809. Crossref

(2012) Global weak solution for a periodic generalized Hunter–Saxton equation. Journal of Mathematical Analysis and Applications 391:2, 530-543. Crossref

(2012) Wave breaking and global existence for the generalized periodic two-component Hunter–Saxton system. Journal of Differential Equations 253:1, 319-355. Crossref

(2012) The dual modified Korteweg-de Vries–Fokas–Qiao equation: Geometry and local analysis. Journal of Mathematical Physics 53:7, 073710. Crossref

(2012) On initial boundary value problems for variants of the Hunter–Saxton equation. Zeitschrift für angewandte Mathematik und Physik 63:3, 441-452. Crossref

(2012) RESTRICTIONS ON THE GEOMETRY OF THE PERIODIC VORTICITY EQUATION. Communications in Contemporary Mathematics 14:03, 1250016. Crossref

(2012) A two-component geodesic equation on a space of constant positive curvature. Journal of Geometry and Physics 62:5, 1298-1308. Crossref

(2012) On the blow-up structure for the generalized periodic Camassa–Holm and Degasperis–Procesi equations. Journal of Functional Analysis 262:7, 3125-3158. Crossref

(2012) GLOBAL WEAK SOLUTIONS FOR A PERIODIC HUNTER–SAXTON EQUATION WITH WEAK DISSIPATION. International Journal of Mathematics 23:04, 1250036. Crossref

(2012) A note on multi-dimensional Camassa–Holm-type systems on the torus. Journal of Physics A: Mathematical and Theoretical 45:12, 125205. Crossref

(2012) Conservative solutions to a system of variational wave equations. Journal of Differential Equations 252:6, 4002-4026. Crossref

(2012) Exact Controllability of Scalar Conservation Laws with an Additional Control in the Context of Entropy Solutions. SIAM Journal on Control and Optimization 50:4, 2025-2045. Abstract | PDF (257 KB) 

(2012) Maximal dissipation in equations of evolution. Journal of Differential Equations 252:1, 567-587. Crossref

(2012) Analyticity of the Cauchy problem for two-component Hunter–Saxton systems. Nonlinear Analysis: Theory, Methods & Applications 75:1, 253-259. Crossref

(2012) Conservative solutions to a nonlinear variational sine-Gordon equation. Journal of Mathematical Analysis and Applications 385:2, 1055-1069. Crossref

(2012) Longitudinal singular response of dusty plasma medium in weak and strong coupling limits. Physics of Plasmas 19:1, 013706. Crossref

(2012) The geometry of a vorticity model equation. Communications on Pure and Applied Analysis 11:4, 1407-1419. Crossref

(2012) On the Cauchy problem of a periodic 2-component -Hunter–Saxton system. Nonlinear Analysis: Theory, Methods & Applications 75:1, 131-142. Crossref

(2012) Global weak solutions to the generalized Proudman-Johnson equation. Communications on Pure and Applied Analysis 11:4, 1387-1396. Crossref

(2012) On the Wave-Breaking Phenomena and Global Existence for the Generalized Periodic Camassa–Holm Equation. International Mathematics Research Notices 2012:21, 4858-4903. Crossref

(2012) FUNCTIONAL REPRESENTATION OF THE NEGATIVE AKNS HIERARCHY. Journal of Nonlinear Mathematical Physics 19:3, 353-372. Crossref

(2012) ON THE NONLOCAL SYMMETRIES OF THE μ-CAMASSA–HOLM EQUATION. Journal of Nonlinear Mathematical Physics 19:3, 411-427. Crossref

2011. Bibliography. Handbook of Nonlinear Partial Differential Equations, Second Edition, 1795-1840. Crossref

(2011) Global weak solutions and smooth solutions for a two-component Hunter-Saxton system. Journal of Mathematical Physics 52:10, 103707. Crossref

(2011) Weak geodesic flow on a semidirect product and global solutions to the periodic Hunter–Saxton system. Nonlinear Analysis: Theory, Methods & Applications 74:15, 4951-4960. Crossref

(2011) Global existence and blow-up phenomena for the periodic Hunter–Saxton equation parametrized by the speed of the Galilean frame. Nonlinear Analysis: Real World Applications 12:5, 2616-2624. Crossref

(2011) The short-wave model for the Camassa–Holm equation: a Riemann–Hilbert approach. Inverse Problems 27:10, 105006. Crossref

(2011) Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves. Journal of Physics A: Mathematical and Theoretical 44:39, 395201. Crossref

(2011) Global Semigroup of Conservative Solutions of the Nonlinear Variational Wave Equation. Archive for Rational Mechanics and Analysis 201:3, 871-964. Crossref

(2011) The matrix Lax representation of the generalized Riemann equations and its conservation laws. Physics Letters A 375:37, 3268-3272. Crossref

(2011) Generalized Euler–Poincaré Equations on Lie Groups and Homogeneous Spaces, Orbit Invariants and Applications. Letters in Mathematical Physics 97:1, 45-60. Crossref

(2011) The curvature of semidirect product groups associated with two-component Hunter–Saxton systems. Journal of Physics A: Mathematical and Theoretical 44:22, 225203. Crossref

(2011) Qualitative behavior and cusped solitons for a partial differential equation. Communications in Nonlinear Science and Numerical Simulation 16:6, 2486-2492. Crossref

(2011) Nonlocal Symmetries and Geometric Integrability of Multi-Component Camassa—Holm and Hunter—Saxton Systems. Chinese Physics Letters 28:5, 050204. Crossref

(2011) The Generalized Proudman–Johnson Equation Revisited. Journal of Mathematical Fluid Mechanics 13:1, 147-154. Crossref

(2011) GENERALIZED CHARACTERISTICS AND THE HUNTER–SAXTON EQUATION. Journal of Hyperbolic Differential Equations 08:01, 159-168. Crossref

(2011) Global existence of dissipative solutions to the Hunter–Saxton equation via vanishing viscosity. Journal of Differential Equations 250:3, 1427-1447. Crossref

(2011) Lipschitz metric for the periodic Camassa–Holm equation. Journal of Differential Equations 250:3, 1460-1492. Crossref

(2011) THE PERIODIC μ-b-EQUATION AND EULER EQUATIONS ON THE CIRCLE. Journal of Nonlinear Mathematical Physics 18:1, 1-8. Crossref

(2011) GLOBAL EXISTENCE AND BLOW-UP PHENOMENA FOR THE PERIODIC HUNTER–SAXTON EQUATION WITH WEAK DISSIPATION. Journal of Nonlinear Mathematical Physics 18:1, 139-149. Crossref

(2010) The even and odd supersymmetric Hunter–Saxton and Liouville equations. Physics Letters A 375:1, 29-35. Crossref

(2010) Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations. Acta Applicandae Mathematicae 112:2, 181-203. Crossref

(2010) The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations. Nonlinearity 23:10, 2517-2537. Crossref

(2010) Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions. Communications in Mathematical Physics 299:1, 129-161. Crossref

(2010) Existence and singularities of solutions to an integrable equation governing short-waves in a long-wave model. Journal of Mathematical Physics 51:9, 093509. Crossref

(2010) The Hunter–Saxton equation: remarkable structures of symmetries and conserved densities. Nonlinearity 23:8, 2009-2028. Crossref

(2010) A two-component μ-Hunter–Saxton equation. Inverse Problems 26:8, 085003. Crossref

(2010) Integrable discretizations for the short-wave model of the Camassa–Holm equation. Journal of Physics A: Mathematical and Theoretical 43:26, 265202. Crossref

(2010) Global and singular solutions to the generalized Proudman–Johnson equation. Journal of Differential Equations 249:2, 392-413. Crossref

(2010) Lipschitz metric for the Hunter–Saxton equation. Journal de Mathématiques Pures et Appliquées 94:1, 68-92. Crossref

(2010) EULER–POINCARÉ FLOWS ON THE LOOP BOTT–VIRASORO GROUP AND SPACE OF TENSOR DENSITIES AND (2 + 1)-DIMENSIONAL INTEGRABLE SYSTEMS. Reviews in Mathematical Physics 22:05, 485-505. Crossref

(2010) Bifurcations and exact bounded travelling wave solutions for a partial differential equation. Nonlinear Analysis: Real World Applications 11:1, 364-371. Crossref

(2010) The Generalized Hunter–Saxton System. SIAM Journal on Mathematical Analysis 42:3, 1286-1304. Abstract | PDF (250 KB) 

(2010) ON THE GEODESIC FLOW ON THE GROUP OF DIFFEOMORPHISMS OF THE CIRCLE WITH A FRACTIONAL SOBOLEV RIGHT-INVARIANT METRIC. Journal of Nonlinear Mathematical Physics 17:1, 7-11. Crossref

(2009) Deltons, peakons and other traveling-wave solutions of a Camassa–Holm hierarchy. Physics Letters A 373:29, 2454-2460. Crossref

(2009) Periodic solitons of an equation for short capillary-gravity waves. Journal of Mathematical Analysis and Applications 352:2, 964-966. Crossref

(2009) Multi-soliton and multi-cuspon solutions of a Camassa–Holm hierarchy and their interactions. Journal of Physics A: Mathematical and Theoretical 42:5, 055203. Crossref

(2009) Local Discontinuous Galerkin Method for the Hunter–Saxton Equation and Its Zero-Viscosity and Zero-Dispersion Limits. SIAM Journal on Scientific Computing 31:2, 1249-1268. Abstract | PDF (582 KB) 

(2009) On the N=2 supersymmetric Camassa–Holm and Hunter–Saxton equations. Journal of Mathematical Physics 50:1, 012704. Crossref

2009. Classification of Monge–Ampeère Equations. Differential Equations - Geometry, Symmetries and Integrability, 223-256. Crossref

(2008) On an integrable two-component Camassa–Holm shallow water system. Physics Letters A 372:48, 7129-7132. Crossref

(2008) Generalized Hunter–Saxton equation and the geometry of the group of circle diffeomorphisms. Mathematische Annalen 342:3, 617-656. Crossref

(2008) Contact linearization of Monge-Ampére equations and Laplace invariants. Doklady Mathematics 78:2, 751-754. Crossref

(2008) Poisson structure of a modified Hunter–Saxton equation. Journal of Physics A: Mathematical and Theoretical 41:28, 285207. Crossref

(2008) Single and multi-solitary wave solutions to a class of nonlinear evolution equations. Journal of Mathematical Analysis and Applications 343:1, 273-298. Crossref

(2008) A Bi-Hamiltonian Supersymmetric Geodesic Equation. Letters in Mathematical Physics 85:1, 55-63. Crossref

(2008) A Contact Linearization Problem for Monge-Ampère Equations and Laplace Invariants. Acta Applicandae Mathematicae 101:1-3, 177-189. Crossref

(2008) The Hunter–Saxton Equation: A Geometric Approach. SIAM Journal on Mathematical Analysis 40:1, 266-277. Abstract | PDF (182 KB) 

(2008) Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation. Journal of Nonlinear Mathematical Physics 15:sup3, 264-276. Crossref

(2008) Algebraic Discretization of the Camassa-Holm and Hunter-Saxton Equations. Journal of Nonlinear Mathematical Physics 15:sup2, 1-12. Crossref

(2007) Riemannian geometry on the diffeomorphism group of the circle. Arkiv för Matematik 45:2, 297-325. Crossref

(2007) Diffractive nonlinear geometrical optics for variational wave equations and the Einstein equations. Communications on Pure and Applied Mathematics 60:10, 1522-1557. Crossref

(2007) The Hunter–Saxton equation describes the geodesic flow on a sphere. Journal of Geometry and Physics 57:10, 2049-2064. Crossref

(2007) Generalized Fourier transform for the Camassa–Holm hierarchy. Inverse Problems 23:4, 1565-1597. Crossref

(2007) On nonlocal symmetries of some shallow water equations. Journal of Physics A: Mathematical and Theoretical 40:17, 4467-4476. Crossref

(2007) The inverse spectral problem for the discrete cubic string. Inverse Problems 23:1, 99-121. Crossref

(2006) Cusp and loop soliton solutions of short-wave models for the Camassa–Holm and Degasperis–Procesi equations. Physics Letters A 359:5, 451-457. Crossref

(2006) Asymptotic Variational Wave Equations. Archive for Rational Mechanics and Analysis 183:1, 163-185. Crossref

(2006) Conservative Solutions to a Nonlinear Variational Wave Equation. Communications in Mathematical Physics 266:2, 471-497. Crossref

(2006) Weak solutions to a nonlinear variational wave equation and some related problems. Applications of Mathematics 51:4, 427-466. Crossref

(2006) SHORT-TIME EXISTENCE FOR SCALE-INVARIANT HAMILTONIAN WAVES. Journal of Hyperbolic Differential Equations 03:02, 247-267. Crossref

(2006) Bihamiltonian Equations on Polynomial Virasoro Algebras. Journal of Nonlinear Mathematical Physics 13:3, 352-364. Crossref

(2006) V ect ( S ¹ ) Action on Pseudodifferential Symbols on S ¹ and (Noncommutative) Hydrodynamic Type Systems. Journal of Nonlinear Mathematical Physics 13:4, 549-565. Crossref

(2006) Wave Breaking in a Class of Nonlocal Dispersive Wave Equations. Journal of Nonlinear Mathematical Physics 13:3, 441-466. Crossref

(2005) Can we always distinguish between positive and negative hierarchies?. Journal of Physics A: Mathematical and General 38:18, L301-L306. Crossref

(2005) The Gurevich–Zybin system. Journal of Physics A: Mathematical and General 38:17, 3823-3840. Crossref

(2005) On the local and nonlocal Camassa–Holm hierarchies. Journal of Mathematical Physics 46:4, 042704. Crossref

(2005) Weak solutions to a nonlinear variational wave equation with general data. Annales de l'Institut Henri Poincaré C, Analyse non linéaire 22:2, 207-226. Crossref

(2005) Global Solutions of the Hunter--Saxton Equation. SIAM Journal on Mathematical Analysis 37:3, 996-1026. Abstract | PDF (287 KB) 

2005. On the Global Weak Solutions to a Variational Wave Equation. Handbook of Differential Equations Evolutionary Equations, 561-648. Crossref

(2004) On the Structure of Solutions to the Periodic Hunter--Saxton Equation. SIAM Journal on Mathematical Analysis 36:1, 272-283. Abstract | PDF (154 KB) 

2003. References. Handbook of Nonlinear Partial Differential Equations. Crossref

(2003) Euler equations on homogeneous spaces and Virasoro orbits. Advances in Mathematics 176:1, 116-144. Crossref

(2003) Continued fractions and integrable systems. Journal of Computational and Applied Mathematics 153:1-2, 47-60. Crossref

(2003) On singularity of a nonlinear variational sine-Gordon equation. Journal of Differential Equations 189:1, 183-198. Crossref

(2003) Discrete Lagrangian systems on the Virasoro group and Camassa Holm family. Nonlinearity 16:2, 683-688. Crossref

(2003) Transformations of solutions for equations and hierarchies of pseudo-spherical type. Journal of Physics A: Mathematical and General 36:8, L125-L132. Crossref

Darryl D. Holm and Martin F. Staley. (2003) Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs. SIAM Journal on Applied Dynamical Systems 2:3, 323-380. Abstract | PDF (12826 KB) 

(2002) Lagrangian time-discretization of the Hunter–Saxton equation. Physics Letters A 304:5-6, 157-167. Crossref

(2002) Потоки Калоджеро - Франсуаза и периодические пиконы. Теоретическая и математическая физика 133:3, 367-385. Crossref

(2001) Inverse scattering solutions of the hunter-saxton equation. Applicable Analysis 78:3-4, 255-269. Crossref

(2001) RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION OF LIQUID CRYSTALS. Communications in Partial Differential Equations 26:3-4, 381-419. Crossref

(2001) Уравнение Калоджеро и уравнения типа Лиувилля. Теоретическая и математическая физика 128:1, 109-115. Crossref

(1999) On the existence and uniqueness of solutions to an asymptotic equation of a variational wave equation. Acta Mathematica Sinica, English Series 15:1, 115-129. Crossref

(1998) Transformations for the Camassa-Holm Equation, Its High-Frequency Limit and the Sinh-Gordon Equation. Journal of the Physical Society of Japan 67:11, 3655-3657. Crossref

(1995) On a nonlinear hyperbolic variational equation: I. Global existence of weak solutions. Archive for Rational Mechanics and Analysis 129:4, 305-353. Crossref

(1995) On a nonlinear hyperbolic variational equation: II. The zero-viscosity and dispersion limits. Archive for Rational Mechanics and Analysis 129:4, 355-383. Crossref

1995. Asymptotic Equations for Nonlinear Hyperbolic Waves. Surveys in Applied Mathematics, 167-276. Crossref

(1994) On a completely integrable nonlinear hyperbolic variational equation. Physica D: Nonlinear Phenomena 79:2-4, 361-386. Crossref