most citedAsymptotic K-soliton-like Solutions of the Zakharov-Kuznetsov type equations

3 citations · 3 across the 4 of their papers we have counts for

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4 papers

math.AP2022

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…

math.AP2022

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…

math.AP2020★ 3 cited

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…

math.AP2020

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…