SOLITARY WAVE SOLUTIONS FOR HIROTA-SATSUMA COUPLED KdV EQUATION AND COUPLED mKdV EQUATION BY DIFFERENTIAL TRANSFORM METHOD

Kangalgil F., Ayaz F.

ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, vol.35, no.2D, pp.203-213, 2010 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 2D
  • Publication Date: 2010
  • Journal Name: ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.203-213
  • Keywords: Two-dimensional differential transform method, solitary wave solutions, coupled KdV and coupled mKdV equations, VARIATIONAL ITERATION METHOD, SYSTEM, SOLVE
  • Dokuz Eylül University Affiliated: No

Abstract

The main aim of this paper is to demonstrate the feasibility and validity of the differential transform method, namely DTM. Therefore, the method has been applied to solve Hirota-Satsuma coupled KdV and coupled mKdV equations with initial conditions of two types. Hence, soliton solutions have been obtained easily as in [9]. The DTM method is based on the Taylor series, but the series coefficients are calculated in an iterative manner by the help of T-transform. For many applications, series converges very quickly and closed form solutions can be reached. In the present work, illustrative examples have showed that the method provides a sequence of functions which converge to the exact solution of the aforementioned systems.