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.
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