Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction
type: Item
instance of: scholarly article
title: Traveling pulses for the Klein-Gordon equation on a lattice or continuum with long-range interaction
zbMATH Open document ID: 1119.34034
published in: Discrete and Continuous Dynamical Systems
publication date: 2007-02-05T00:00:00Z
review text: The authors consider the nonlocal wave equation \[ u_{tt}-\frac{1}{\varepsilon^2}(j_{\varepsilon}*u-u)+f(u) =0,\eqno(1) \] for \(t>0\) and \(x\in \mathbb{R}\), where \(*\) is a continuous or discrete convolution and \(f\) is a \(C^2\) function with \(f(0)=0\). The also consider a lattice version of \((1)\), i.e., \[ \ddot{u}_n- \frac{1}{\varepsilon^2}\sum_{k=-\infty}^{\infty}\alpha_ku_{n-k}+f(u_n)=0\eqno(2) \] for \(n\in \mathbb{Z}\), and they study the homoclinic traveling wave solutions of both \((1)\) and \((2)\), which decay at infinity.
reviewed by: Ioan I. Vrabie
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37L60
Mathematics Subject Classification ID: 34A35
zbMATH DE Number: 5121858
zbMATH Keywords: Klein-Gordon lattice
zbMATH Keywords: nonlocal wave equation
zbMATH Keywords: nonlinear pulses
author: Peter W. Bates
author: Chun-Lei Zhang
MaRDI profile type: Publication
full work available at URL: dcds.2006.16.235
OpenAlex ID: W2017095213
DOI: 10.3934/DCDS.2006.16.235
Recommended article: Q3611263
Recommended article: Multi-travelling waves for the nonlinear Klein-Gordon equation
Recommended article: Kink-like periodic travelling waves for lattice equations with on-site and inter-site potentials
Recommended article: Travelling waves for an infinite lattice Multibump type solutions
Recommended article: Traveling Wavefronts in Lattice Differential Equations with Time Delay and Global Interaction
Recommended article: Traveling waves in time periodic lattice differential equations
Recommended article: Q4656031
Recommended article: Travelling waves for the Gross-Pitaevskii equation in dimension larger than two
Recommended article: Q5354573
Recommended article: New distributional travelling waves for the nonlinear Klein-Gordon equation.
description: scientific article; zbMATH DE number 5121858