Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation

Abstract

We prove the asymptotic stability of a finite sum of well-ordered solitary waves for the Zakharov-Kuznetsov equation in dimensions two and three. Moreover, we derive a qualitative version of the orbital stability result which turns out to be useful for the study of the collision of two solitary waves. The proof extends the ideas of Martel, Merle and Tsai for the sub-critical gKdV equation in dimension one to the higher-dimensional case. It relies on monotonicity properties on oblique half-spaces and rigidity properties around one solitary wave introduced by Côte, Muñoz, Pilod and Simpson in dimension two, and by Farah, Holmer, Roudenko and Yang in dimension three.

arXiv comment32 pages, 7 figures

References in corpus (7)

• The Fourier restriction norm method for the Zakharov-Kuznetsov equation
• Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons
• From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov
• A liouville property with application to asymptotic stability for the camassa-holm equation
• Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
• Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation
• Dynamics of the collision of two nearly equal solitary waves for the Zakharov-Kuznetsov equation

Cited by in corpus (1)

• Dynamics of the collision of two nearly equal solitary waves for the Zakharov-Kuznetsov equation