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2013 The Bäcklund Transformations, Exact Solutions, and Conservation Laws for the Compound Modified Korteweg-de Vries-Sine-Gordon Equations which Describe Pseudospherical Surfaces
S. M. Sayed
J. Appl. Math. 2013: 1-7 (2013). DOI: 10.1155/2013/613065

Abstract

I show that the compound modified Korteweg-de Vries-Sine-Gordon equations describe pseudospherical surfaces, that is, these equations are the integrability conditions for the structural equations of such surfaces. I obtain the self-Bäcklund transformations for these equations by a geometrical method and apply the Bäcklund transformations to these solutions and generate new traveling wave solutions. Conservation laws for the latter ones are obtained using a geometrical property of these pseudospherical surfaces.

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S. M. Sayed. "The Bäcklund Transformations, Exact Solutions, and Conservation Laws for the Compound Modified Korteweg-de Vries-Sine-Gordon Equations which Describe Pseudospherical Surfaces." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/613065

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.37036
MathSciNet: MR3035175
Digital Object Identifier: 10.1155/2013/613065

Rights: Copyright © 2013 Hindawi

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