Hostname: page-component-788cddb947-wgjn4 Total loading time: 0 Render date: 2024-10-13T23:41:07.826Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-integrable lattice equations supporting kink and soliton solutions

Published online by Cambridge University Press:  31 January 2002

A. K. COMMON  and
M. MUSETTE
A. K. COMMON
Affiliation:
Institute of Mathematics and Statistics, Cornwallis Building, University of Kent, Canterbury, Kent CT2 7NF, UK
M. MUSETTE
Affiliation:
Dienst Theoretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonintegrable differential-difference equations are constructed which support two-kink and two-soliton solutions. These equations are related to the discrete Burgers hierarchy and a discrete form of the Korteweg-de Vries equation. In particular, discretisations of equations related to the Fitzhugh-Nagumo-Kolmogorov-Petrovskii-Piskunov, Satsuma-Burgers-Huxley equations are derived. Methods presented here can also be used to derive non-integrable differential-difference equations describing the elastic collision of more than two kinks or solitary waves.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 12 , Issue 6 , December 2001 , pp. 709 - 718
Copyright
2001 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)