Travelling wave solutions for a generalized Boussinesq equation by using free software

Authors:
Maria Luz Gandarias;Maria Santos Bruzón
Affiliations:
University of Cádiz, Department of Mathematics, Puerto Real, Cádiz, Spain;University of Cádiz, Department of Mathematics, Puerto Real, Cádiz, Spain
Venue:
SEPADS'10 Proceedings of the 9th WSEAS international conference on Software engineering, parallel and distributed systems
Year:
2010

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Abstract

One of the more interesting solutions of the Boussinesq equation are the soliton solutions. We previously derived a complete group classification for a generalized Boussinesq (GB) equation. In this paper we first show how the recently free software MAXIMA program symmgrp2009.max derived by W. Heremann can be used to calculate the determining equations for the classical symmetries of the GB equation. Using classical Lie symmetries, we now consider traveling-wave reductions. The corresponding solutions of the generalized Boussinesq equation exhibit solitary waves and bound states.