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In this paper, the simplest equation method is implemented to construct exact traveling-wave solutions to the modified Fornberg-Whitham equation. With the help of Mathematica symbolic computa- tion software, some new classes of explicit exact solutions are derived. Graphical representations of some obtained solutions are displayed. The method demonstrates the applicability, reliability and efficiency in treating a wide range of nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The aim of the present analysis is to generalize the recently devised technique, known as the residual power series method (RPSM), for analytic treatment of higher-order non-linear partial differential equations (NPDEs). This method based on constructing series solutions in a form of rapidly convergent series with easily computable components and without need of linearization, discretization, perturbation or unrealistic assumptions. Convergence and error analysis are discussed in details. To illustrate the efficiency, reliability and simplicity of proposed method, exact solutions for some diffusion processes of power, rational and exponential law diffusivities are obtained. [ABSTRACT FROM AUTHOR]