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Symmetries of generalized Klein-Gordon (including sine-Gordon) equations in three or more dimensions

Published online by Cambridge University Press:  24 October 2008

T. J. Gordon
T. J. Gordon
Affiliation:
Department of Engineering Mathematics, Loughborough University of Technology
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Extract

Much recent attention has been devoted to those nonlinear partial differential equations admitting higher-order conservation laws (e.g. [2] and references therein) or equivalently admitting higher-order symmetries. In particular the sine-Gordon equation possesses such symmetries [5, 7] where is the two-dimensional d'Alembertian operator. The question posed and solved here is whether such behaviour is possible in higher dimensions. We therefore consider the ‘Generalized Klein–Gordon’ (GKG) equation

in N dimensions where and N ≥ 3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 101 , Issue 2 , March 1987 , pp. 343 - 348
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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