APPLICATION OF DIFFERENTIAL TRANSFORMATION METHOD TO THE DULLIN-GOTTWALD-HOLM EQUATION

Nonlinear problems in partial differential equations are open problems in many fields of mathematics and engineering. So associated with the structure of the problems, many analytical and numerical methods are obtained. We show that the differential transformation method is an appropriate method for the Dullin-Gottwald-Holm equation (DGH), which is a nonlinear partial differential equation arise in many physical phenomena. Hence in this paper, the differential transform method (DTM) is applied to the Dullin-Gottwald- Holm equation. We obtain the exact solutions of Dullin-Gottwald-Holm equation by using the DTM. In addition, we give some examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equations. These results show that this technique is easy to apply and provide a suitable method for solving differential equations. To our best knowledge, the theorem presented in Section 2 has been not introduced previously. We presented and proved this new theorem which can be very effective for formulating the nonlinear forms of partial differential equations.