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Abstract and Applied Analysis
Volume 2013, Article ID 693076, 13 pages
Research Article

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

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 8 January 2013; Accepted 10 March 2013

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.


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.