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International Journal of Differential Equations
Volume 2011, Article ID 545607, 15 pages
Research Article

Solving Famous Nonlinear Coupled Equations with Parameters Derivative by Homotopy Analysis Method

Department of Applied Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91779-48974, Iran

Received 15 May 2011; Accepted 4 July 2011

Academic Editor: Shaher M. Momani

Copyright © 2011 Sohrab Effati 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.


The homotopy analysis method (HAM) is employed to obtain symbolic approximate solutions for nonlinear coupled equations with parameters derivative. These nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The efficiency and accuracy of the method are verified by using two famous examples: coupled Burgers and mKdV equations. The obtained results show that the homotopy perturbation method is a special case of homotopy analysis method.