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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. (English) Zbl 1141.65382

Summary: 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 Korteweg de Vries (KdV) and modified KdV equations are given to show the effectiveness of the coupled VIM-Laplace-Padé and VIM-Padé techniques.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A10 Laplace transform
41A21 Padé approximation
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