Reduced Differential Transform Method and Its Application on Kawahara Equations

In this paper, the reduced form of differential transform method (called reduced DTM), is employed to approximate the solutions of Kawahara and modified Kawahara equations. These equations, proposed first by Kawahara [T. Kawahara, Oscillatory solitary waves in dispersive media, J. Phys. Soc. Jpn. 33 (1972) 260–264.] in 1972, occurs in the theory of shallow water waves and plays an important role in the modeling of many physical phenomena such as plasma waves, magneto–acoustic wave. In the last few years, considerable efforts have been expended in formulating accurate and efficient methods to solve these equations. In this paper, we first present the two–dimensional reduced DTM then employ to approximate solutions of the Kawahara and modified Kawahara equations. This method provides remarkable accuracy for the approximate solutions when compared to the exact solutions, especially in large scale domain. Numerical results demonstrate that the methods provide efficient approaches to solving these equations.