Construction and characterization of solutions converging to solitons for supercritical gKdV equations.

zbMath1240.35433arXiv0907.5486MaRDI QIDQ636908

Vianney Combet

Publication date: 1 September 2011

Published in: Differential and Integral Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.5486

zbMATH Keywords

nonlinear Schrödinger equationsolitongeneralized Korteweg-de Vries equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Soliton solutions (35C08)

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Strongly interacting multi-solitons with logarithmic relative distance for the gKdV equation ⋮ Instability of Solitons in the 2d Cubic Zakharov-Kuznetsov Equation ⋮ Stability and instability of the KdV solitary wave under the KP-I flow ⋮ Dynamics near the solitary waves of the supercritical gKDV equations ⋮ High-speed excited multi-solitons in nonlinear Schrödinger equations ⋮ On asymptotic stability of nonlinear waves ⋮ Instability of solitons–revisited, I: The critical generalized KdV equation ⋮ Instability of solitons–revisited, II: The supercritical Zakharov-Kuznetsov equation ⋮ On existence and uniqueness of asymptotic \(N\)-soliton-like solutions of the nonlinear Klein-Gordon equation ⋮ Multi-solitons and Related Solutions for the Water-waves System

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