Journal of Applied Mathematics
Volume 2008 (2008), Article ID 576783, 10 pages
doi:10.1155/2008/576783
Research Article

Travelling Wave Solutions for the KdV-Burgers-Kuramoto and Nonlinear Schrödinger Equations Which Describe Pseudospherical Surfaces

S. M. Sayed,1,2 O. O. Elhamahmy,3 and G. M. Gharib2

1Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
2Mathematics Department, Tabouk Teacher College, Tabouk University, Ministry of Higher Education, P.O. Box 1144, Tabouk, Saudi Arabia
3Mathematics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt

Received 23 February 2008; Revised 18 May 2008; Accepted 13 August 2008

Academic Editor: Bernard Geurts

Copyright © 2008 S. M. Sayed et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations with constant Gaussian curvature −1. Travelling wave solutions for the above equations are obtained by using a sech-tanh method and Wu's elimination method.