Modulation theory for radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation

DOI10.1007/S00332-022-09859-WzbMath1505.35322OpenAlexW4309583070MaRDI QIDQ2105222

Noel F. Smyth, Lu Trong Khiem Nguyen

Publication date: 8 December 2022

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-022-09859-w

zbMATH Keywords

sine-Gordon equationmodulation theorykink wavesreturning effect

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Soliton equations (35Q51) Soliton solutions (35C08)

Uses Software

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Cites Work

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• Slope modulation of waves governed by sine-Gordon equation
• Kinks and the minimal surface equation in Minkowski space
• Evolution of two-dimensional standing and travelling breather solutions for the sine-Gordon equation
• A numerical scheme and some theoretical aspects for the cylindrically and spherically symmetric sine-Gordon equations
• Slope modulation of ring waves governed by two-dimensional sine-Gordon equation
• Metastable stationary solutions of the radiald-dimensional sine-Gordon model
• Ring-Shaped Quasi-Soliton Solutions to the Two- and Three-Dimensional Sine-Gordon Equation
• A general approach to linear and non-linear dispersive waves using a Lagrangian
• Pulse evolution for a two-dimensional sine-Gordon equation

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