We present a large-amplitude existence theory for two-dimensional solitary waves propagating through a two layer body of water. The domain of the fluid is bounded below by an impermeable flat ocean floor and above by a free boundary at constant pressure. For any piecewise smooth upstream density distribution and laminar background current, we construct a global curve of solutions. This curve bifurcates from the background current and, following along the curve, we find waves that are arbitrarily close to having horizontal stagnation points. The small-amplitude waves are constructed using a center manifold reduction technique. The large-amplitude theory is obtained through analytical global bifurcation together with refined qualitative properties of the waves.


  1. water waves
  2. global bifurcation
  3. solitary waves
  4. stratification
  5. internal waves

MSC codes

  1. 35B32
  2. 35Q31
  3. 35J60
  4. 35J66
  5. 76B15
  6. 76B55

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Information & Authors


Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 4812 - 4864
ISSN (online): 1095-7154


Submitted: 1 December 2020
Accepted: 27 April 2021
Published online: 30 August 2021


  1. water waves
  2. global bifurcation
  3. solitary waves
  4. stratification
  5. internal waves

MSC codes

  1. 35B32
  2. 35Q31
  3. 35J60
  4. 35J66
  5. 76B15
  6. 76B55



Funding Information

National Science Foundation https://doi.org/10.13039/100000001 : DMS-1812436

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