Bifurcations and stability of internal solitary waves
Abstract
We study both supercritical and subcritical bifurcations of internal solitary waves propagating along the interface between two deep ideal fluids. We derive a generalized nonlinear Schrödinger equation to describe solitons near the critical density ratio corresponding to transition from subcritical to supercritical bifurcation. This equation takes into account gradient terms for the four-wave interactions (the so-called Lifshitz term and a nonlocal term analogous to that first found by Dysthe for pure gravity waves), as well as the six-wave nonlinear interaction term. Within this model, we find two branches of solitons and analyze their Lyapunov stability.
- Publication:
-
Soviet Journal of Experimental and Theoretical Physics Letters
- Pub Date:
- May 2006
- DOI:
- 10.1134/S0021364006050043
- Bibcode:
- 2006JETPL..83..201A
- Keywords:
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- 05.45.Yv;
- 47.55.-t;
- 47.90.+a