10 citations · 20 across the 6 of their papers we have counts for
6 papers
Dynamics of the collision of two nearly equal solitary waves for the Zakharov-Kuznetsov equation
Didier Pilod, Frédéric Valet
We study the dynamics of the collision of two solitary waves for the Zakharov-Kuznetsov equation in dimension and . We describe the evolution of the solution behaving as a s…
Asymptotic stability of a finite sum of solitary waves for the Zakharov-Kuznetsov equation
Didier Pilod, Frédéric Valet
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…
Decay of solitary waves of fractional Korteweg-de Vries type equations
Arnaud Eychenne, Frédéric Valet
We study the solitary waves of fractional Korteweg-de Vries type equations, that are related to the -dimensional semi-linear fractional equations: \begin{align*} \vert D \vert^α…
Strongly interacting solitary waves for the fractional modified Korteweg-de Vries equation
Arnaud Eychenne, Frédéric Valet
We study one particular asymptotic behaviour of a solution of the fractional modified Korteweg-de Vries equation (also known as the dispersion generalised modified Benjamin-Ono equ…
Asymptotic K-soliton-like Solutions of the Zakharov-Kuznetsov type equations
Frédéric Valet
We study here the Zakharov-Kuznetsov equation in dimension and and the modified Zakharov-Kuznetsov equation in dimension . Those equations admit solitons, characterized…
Polynomial Growth of high Sobolev Norms of solutions to the Zakharov-Kuznetsov Equation
Raphaël Cote, Frédéric Valet
We consider the Zakharov-Kuznetsov equation (ZK) in space dimension 2. Solutions u with initial data u\_0 H s are known to be global if s 1. We prove that for any integ…