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Symmetry group analysis and similarity solutions of the CBS equation in (2+1) dimensions
Author(s) -
Gandarias M.L.,
Bruzon M.S.
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810591
Subject(s) - homogeneous space , integrable system , symmetry (geometry) , similarity (geometry) , variety (cybernetics) , group (periodic table) , mathematical physics , pure mathematics , function (biology) , symmetry group , mathematics , lie group , mathematical analysis , physics , quantum mechanics , geometry , computer science , image (mathematics) , statistics , artificial intelligence , evolutionary biology , biology
We consider the (2+1)—dimensional integrable Calogero—Bogoyavlenskii—Schiff (CBS) written in a potential form. By using classical Lie symmetries, we consider 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 solitary waves and bound states. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)