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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.

65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
35A22Transform methods (PDE)
44A10Laplace transform
41A21Padé approximation
Full Text: DOI
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