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In this research paper, we develop a new method called the Natural Decomposition Method (NDM) for solving coupled system of nonlinear partial differential equations (CSNLPDEs). The new method is a combination of the Natural Transform Method (NTM) and the Adomian Decomposition Method (ADM). By using the new method, we successfully handle some class of cou- pled system of nonlinear partial differential equations (CSNLPDEs) in a simple and elegant way. The proposed method gives an exact or approximate solution in the form of a rapid convergence series. Hence, the Natural Decomposition Method (NDM) is an excellent mathematical tool for solving linear and nonlin- ear differential equation. Thus, NDM can easily be used to solve a wide class of nonlinear partial differential equations (NLPDEs) and obtain an exact or analytical solution.

SOLVING COUPLED SYSTEM OF NONLINEAR PDE'S USING THE NATURAL DECOMPOSITION METHOD