Stability and instability of the KdV solitary wave under the KP-I flow

Frédéric Rousset (1) , Nikolay Tzvetkov (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

We consider the KP-I and gKP-I equations in $\mathbb{R}\times (\mathbb{R}/2\pi \mathbb{Z})$. We prove that the KdV soliton with subcritical speed $0

Mots clés: transverse nonlinear instability; equations; solitons

Domaines: Equations aux dérivées partielles [math.AP]

Frédéric Rousset, Nikolay Tzvetkov. Stability and instability of the KdV solitary wave under the KP-I flow. Communications in Mathematical Physics, 2012, 313 (1), pp.155-173. ⟨10.1007/s00220-012-1495-y⟩. ⟨hal-00707829⟩