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SIAM J. Appl. Math. 72, pp. 240-260 (21 pages)
Nonlinear Waves in Shallow Honeycomb Lattices
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Add to FacebookThe linear spectrum and corresponding Bloch modes of shallow honeycomb lattices near Dirac points are investigated. Via perturbation theory, the dispersion relation is found to have threefold degeneracy at leading order with eigenvalue splitting at the following two orders; i.e., the threefold eigenvalue splits into single and double values. Multiscale perturbation methods are employed to describe the nonlinear dynamics of the associated wave envelopes. The dynamics of the envelope depends on different asymptotic balances whereupon a three-level nonlinear Dirac-type equation or a two-level nonlinear Dirac equation is derived. The analysis agrees well with direct numerical simulations.
© 2012 Society for Industrial and Applied Mathematics
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Received March 07, 2011
Accepted November 14, 2011
Published online January 26, 2012
Accepted November 14, 2011
Published online January 26, 2012
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