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Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method. (English) Zbl 0992.35092
Summary: We propose a reliable algorithm to develop exact and approximate solutions for the nonlinear dispersive KdV equation with initial profile. The approach rests mainly on Adomian decomposition method. The single soliton, the two-soliton and rational solutions are obtained by this method. Numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

35Q53KdV-like (Korteweg-de Vries) equations
35C05Solutions of PDE in closed form
35A25Other special methods (PDE)
37K40Soliton theory, asymptotic behavior of solutions
Full Text: DOI
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