The Bäcklund Transformations, Exact Solutions, and Conservation Laws for the Compound Modified Korteweg-de Vries-Sine-Gordon Equations which Describe Pseudospherical Surfaces-Reference-Cited by-同舟云学术

The Bäcklund Transformations, Exact Solutions, and Conservation Laws for the Compound Modified Korteweg-de Vries-Sine-Gordon Equations which Describe Pseudospherical Surfaces

Published:2013 Issue: Volume:2013 Page:1-7
ISSN:1110-757X
Container-title:Journal of Applied Mathematics
language:en
Short-container-title:Journal of Applied Mathematics

Author:

Sayed S. M.¹²

Affiliation:

1. Mathematics Department, Faculty of Science, Tabouk University, Tabouk, Saudi Arabia

2. Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

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.

Publisher

Hindawi Limited

Subject

Applied Mathematics

Link

http://downloads.hindawi.com/journals/jam/2013/613065.pdf

Reference35 articles.

1. Bäcklund Transformations and Inverse Scattering Solutions for Some Pseudospherical Surface Equations

2. Pseudospherical Surfaces and Evolution Equations

3. The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems

4. Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II

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