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VOLUME 83 (2006) | ISSUE 5 | PAGE 241
Bifurcations and stability of internal solitary waves
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.