Abstract
An extended homogeneous balance method is suggested in this paper. Based on computerized symbolic computation and the homogeneous balance method, new exact traveling wave solutions of nonlinear partial differential equations (PDEs) are presented. The shallow-water equations represent a simple yet realistic set of equations typically found in atmospheric or ocean modeling applications, we consider the exact solutions of the nonlinear generalized shallow water equation and the fourth order Boussinesq equation. Applying this method, with the aid of Mathematica, many new exact traveling wave solutions are successfully obtained.
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