A direct approach to studying soliton perturbations

DOI10.1088/0305-4470/23/12/017zbMath0725.35088OpenAlexW2048904955MaRDI QIDQ5201678

Russell L. Herman

Publication date: 1990

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/23/12/017

zbMATH Keywords

sine-Gordon equationsinverse scattering theoryone-soliton solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51)

Related Items (25)

Eigenfunctions of Linearized Integrable Equations Expanded Around an Arbitrary Solution ⋮ Soliton perturbation theory for a higher order Hirota equation ⋮ Perturbation theory for nearly integrable multicomponent nonlinear PDEs ⋮ Soliton dynamics for near integrable differential-difference equations ⋮ Soliton perturbation theory for matrix complex modified Korteweg-de Vries equation ⋮ Dynamical Behavior of Two-Soliton Solution Exhibited by Perturbed Sine-Gordon Equation ⋮ Gauge equivalent structure and solitary wave solution for a modified Landau-Lifshitz equation ⋮ Damped Kadomtsev–Petviashvili Equation for Weakly Dissipative Solitons in Dense Relativistic Degenerate Plasmas ⋮ Perturbed soliton solutions for an integral modified KdV equation ⋮ The perturbed Korteweg–de Vries equation considered anew ⋮ The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy. ⋮ Solitary wave interaction and evolution for a higher-order Hirota equation ⋮ Complete eigenfunctions of linearized integrable equations expanded around a soliton solution ⋮ Broer-Kaup system with corrections via inverse scattering transform ⋮ Direct approach of perturbation theory for kink solitons ⋮ A simple treatment of the sine-Gordon equation ⋮ Perturbations of dark solitons ⋮ Perturbed soliton excitations in the DNA double helix ⋮ Exploring the connection between quasistationary and squared eigenfunction expansion techniques in soliton perturbation theory ⋮ Squared eigenfunctions for the Sasa–Satsuma equation ⋮ Numerical realizations of solutions of the stochastic KdV equation ⋮ The perturbed sine-Gordon breather equation integrated by Riemann's method ⋮ Structure of linearization operators of the Korteweg-de Vries hierarchy equations expanded around single-soliton solutions ⋮ The renormalization method for singular perturbation of solitons ⋮ Integrable theory of the perturbation equations.

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