The major goal of this study is to deal with the coupled system of nonlinear long wave equations under the effects of dissipation. Reduced differential transform method which is a semi analytical approach is employed to find out the solution of the coupled system. Reduced differential transform method is mainly designed to calculate the approximate solution in the form of convergent power series by simple, easy and straightforward process. In the framework of reduced differential transform method, many nonlinear coupled problems had been solved which did not have the mixed partial derivatives. To solve a nonlinear coupled system containing mixed partial derivatives is not an easy task. Particularly, the current study is based on such type of nonlinear system. Using Maple, the numerical results are computed, and the program is executed several times by taking different intervals of time to determine the efficiency and appropriateness of the suggested technique. The numerical and graphical results for the coupled system of the nonlinear long wave equations with dissipation effects are calculated. The result shows that reduced differential transformed method is turned to be a very reliable and efficient technique.

Keywords: Differential Transform Method, System of Nonlinear, Long Wave Equations, Dissipation Effects