Symplectic computation of solitary waves for general sine-Gordon equations
type: Item
instance of: scholarly article
title: Symplectic computation of solitary waves for general sine-Gordon equations
zbMATH Open document ID: 0987.65132
DOI: 10.1016/S0378-4754(00)00300-1
author: Xiaowu Lu
published in: Mathematics and Computers in Simulation
publication date: 2002-06-09T00:00:00Z
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 37K45
zbMATH DE Number: 1619793
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: topological stability
zbMATH Keywords: symplectic schemes
zbMATH Keywords: sine-Gordon equation
zbMATH Keywords: solitary waves
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
cites work: Q4167627
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Wikidata QID: Q126552150
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review text: The paper presents a class of symplectic schemes for the numerical computation of the solutions of the sine-Gordon equation: NEWLINE\[NEWLINE\partial_t^2u- \partial_x^2u+ g(u)= 0, \qquad (x,t)\in \mathbb{R}\times (0,\infty).NEWLINE\]NEWLINE It is demonstrated that these schemes preserve the long-time global structure and the topological stabilities of solitary waves. Numerical experiments show that such symplectic schemes are suitable tools for the numerical computation and investigation of the global geometric structure for the solution of general sine-Gordon type systems, reproducing most of the structure of interest.
description: scientific article; zbMATH DE number 1619793