Abstract and Applied Analysis
Volume 2013 (2013), Article ID 349173, 10 pages
http://dx.doi.org/10.1155/2013/349173
Research Article

The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions

Shoukry Ibrahim Atia El-Ganaini1,2

1Mathematics Department, Faculty of Science, Damanhour University, Bahira 22514, Egypt
2Mathematics Department, Faculty of Science and Humanity Studies at Al-Quwaiaiah, Shaqra University, Al-Quwaiaiah 11971, Saudi Arabia

Received 19 October 2012; Accepted 30 December 2012

Academic Editor: Elena Litsyn

Copyright © 2013 Shoukry Ibrahim Atia El-Ganaini. 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

The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1)-dimensional hyperbolic nonlinear Schrodinger (HNLS) equation, the generalized nonlinear Schrodinger (GNLS) equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.