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In this article, we apply the new generalized (G′/G)-expansion method to solve two nonlinear partial differential equations and construct traveling wave solutions in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. We underline the power of the new generalized (G′/G)-expansion method in providing generalized solitary wave solutions of different physical structures. It is shown that the new generalized (G′/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear partial differential equation systems in mathematical physics and engineering.