## Abstract and Applied Analysis

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

Shoukry Ibrahim Atia El-Ganaini

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 349173, 10 pages.

Dates
First available in Project Euclid: 18 April 2013

https://projecteuclid.org/euclid.aaa/1366306749

Digital Object Identifier
doi:10.1155/2013/349173

Mathematical Reviews number (MathSciNet)
MR3034950

Zentralblatt MATH identifier
1308.35048

#### Citation

El-Ganaini, Shoukry Ibrahim Atia. The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions. Abstr. Appl. Anal. 2013 (2013), Article ID 349173, 10 pages. doi:10.1155/2013/349173. https://projecteuclid.org/euclid.aaa/1366306749

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