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

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.