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Symmetries of generalized Klein–Gordon (including sine-Gordon) equations in two 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 attention has been devoted over the years to the sine-Gordon equation φuv = sin φ (e.g. [2] and references therein). Of fundamental significance is the existence of a countably infinite set of conservation laws, which arises from a corresponding set of symmetries (e.g. [6, 7]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 3 , November 1987 , pp. 573 - 586
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

REFERENCES

[1]Clarkson, P. A., McLeod, J. B., Olver, P. J. and Ramani, A.. Integrability of Klein–Gordon equations. SIAM J. Math. Anal. 17 (1986), 798–802.CrossRefGoogle Scholar
[2]Dodd, R. K., Eilbeck, J. C., Gibbon, J. D. and Morris, H. C.. Solitons and nonlinear wave equations (Academic Press, 1982).Google Scholar
[3]Fordy, A. P. and Gibbons, J.. Nonlinear Klein–Gordon equations and Toda lattices. Commun. Math. Phys. 77 (1980), 21–30.CrossRefGoogle Scholar
[4]Gordon, T. J.. Symmetries of generalized Klein–Gordon (including sine-Gordon) equations in three or more dimensions. Math. Proc. Cambridge Philos. Soc. 101 (1987), 343–348.CrossRefGoogle Scholar
[5]Mikhailov, A. V.. Integrability of a two dimensional generalisation of the Toda chain. Soviet. Phys. JETP Lett. 30 (1979), 414–418.Google Scholar
[6]Olver, P. J.. Evolution equations possessing infinitely many symmetries. J. Math. Phys. 18 (1977), 1212–1215.CrossRefGoogle Scholar
[7]Tu, G. Z.. On polynomial symmetries of the sine-Gordon equation. Math. Proc. Cambridge Philos. Soc. 91 (1982), 485–489.CrossRefGoogle Scholar