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VOLUME 83 | ISSUE 5 | PAGE 241
Bifurcations and stability of internal solitary waves
D. S. Agafontsev, F. Dias+, E. A. Kuznetsov
L.D. Landau Institute of Theoretical Physics, 119334 Moscow, Russia
+Centre de Mathématiques et de Leurs Applications, Ecole Normale Supérieure de Cachan, 94235 Cachan cedex, France


PACS: 05.45.Yv, 47.55.-t, 47.90.+a
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.


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