## Abstract and Applied Analysis

### New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

Shoukry Ibrahim Atia El-Ganaini

#### Abstract

The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. 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. This method can also be applied to nonintegrable equations as well as integrable ones.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 693076, 13 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393511863

Digital Object Identifier
doi:10.1155/2013/693076

Mathematical Reviews number (MathSciNet)
MR3049327

Zentralblatt MATH identifier
1291.35281

#### Citation

El-Ganaini, Shoukry Ibrahim Atia. New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method. Abstr. Appl. Anal. 2013 (2013), Article ID 693076, 13 pages. doi:10.1155/2013/693076. https://projecteuclid.org/euclid.aaa/1393511863

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