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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
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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

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