Travelling wave solutions for a CBS equation in 2 + 1 dimensions

Authors:
Maria Luz Gandarias;Maria Santos Bruzon
Affiliations:
University of Cádiz, Department of Mathematics, Cádiz, Spain;University of Cádiz, Department of Mathematics, Cádiz, Spain
Venue:
MATH'08 Proceedings of the American Conference on Applied Mathematics
Year:
2008

Citing 1
Cited 2

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Abstract

One of the more interesting solutions of the (2 + 1)-dimensional integrable Calogero-Bogoyavlenskii-Schiff (CBS) equation are the soliton solutions. We previously derived a complete group classification for the CBS in (2 +1)-dimensions written as a system of partial differential equations. We now consider the classical Lie symmetries of the CBS equation written in a potential form. We obtain travelling-wave reductions with variable velocity depending on the form of an arbitrary function. The corresponding solutions of the (2 + 1)-dimensional equation involve arbitrary smooth functions. Consequently the solutions exhibit a rich variety of qualitative behaviours. Indeed by making adequate choices for the arbitrary functions, we exhibit periodic and solitary waves.