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Solitary wave solutions for the KdV and mKdV equations by differential transform method. (English) Zbl 1198.35222

Summary: We aim to present a reliable algorithm in order to obtain exact and approximate solutions for the nonlinear dispersive KdV and mKdV equations with initial profile. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. We first present the definition and operation of the two-dimensional differential transform and investigate the soliton solutions of Kdv and mKdV equations are obtained by the present method. Therefore, in the present work, numerical examples are tested to illustrate the pertinent feature of the proposed algorithm.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations