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Transverse nonlinear instability for two-dimensional dispersive models. (English) Zbl 1169.35374
Summary: We present a method to prove nonlinear instability of solitary waves in dispersive models. Two examples are analyzed: we prove the nonlinear long time instability of the KdV solitary wave (with respect to periodic transverse perturbations) under a Kadomtsev-Petviashvili-I flow and the transverse nonlinear instability of solitary waves for the cubic nonlinear Schrödinger equation.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
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