Transverse nonlinear instability for two-dimensional dispersive models

Frédéric Rousset (1, 2) , Nikolay Tzvetkov

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 IRMAR - Institut de Recherche Mathématique de Rennes

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 KP-I flow and the transverse nonlinear instability of solitary waves for the cubic nonlinear Schrodinger equation. (c) 2008 Elsevier Masson SAS. All rights reserved.

Mots clés: Kadomtsev-Petviashvili equation; solitary waves; Shrödinger-equations; stability; solitons

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Rousset, Nikolay Tzvetkov. Transverse nonlinear instability for two-dimensional dispersive models. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2009, 26 (2), pp.477-496. ⟨10.1016/j.anihpc.2007.09.006⟩. ⟨hal-00458107⟩