Abstract
This chapter deals with the theory and applications of nonlinear Klein-Gordon and sine-Gordon equations. Special emphasis is given to various methods of solutions of these equations. The Green’s function method combined with integral transforms is employed to solve the linear Klein-Gordon equation. The Whitham averaging procedure and the Whitham averaged Lagrangian principle are used to discuss solutions of the nonlinear Klein-Gordon equation. Included are different ways of finding general and particular solutions of the sine-Gordon equation. Special attention is given to solitons, antisolitons, breather solutions, energy associated with them, interaction of solitons, Bäcklund transformations, similarity solutions, and the inverse scattering method. Significant features of these methods and solutions are described with other ramifications.
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© 1997 Springer Science+Business Media New York
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Debnath, L. (1997). Nonlinear Klein-Gordon and Sine-Gordon Equations. In: Nonlinear Partial Differential Equations for Scientists and Engineers. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-2846-7_11
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DOI: https://doi.org/10.1007/978-1-4899-2846-7_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-2848-1
Online ISBN: 978-1-4899-2846-7
eBook Packages: Springer Book Archive