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Exact solutions of some nonlinear partial differential equations using the variational iteration method linked with Laplace transforms and the Padé technique

✍ Scribed by Tamer A. Abassy; Magdy A. El-Tawil; H. El-Zoheiry

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 666 KB
Volume: 54
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2006.12.067

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✦ Synopsis

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger's equation, compacton k(n, n) equation, Zakharov-Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM-Laplace-Padé and VIM-Padé techniques.

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The purpose of this study is to introduce a modification of the homotopy perturbation method using Laplace transform and Padé approximation to obtain closed form solutions of nonlinear coupled systems of partial differential equations. Two test examples are given; the coupled nonlinear system of Bur