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The new generalized (G′/G)-expansion method is an interesting approach to find new and more general exact solutions to the nonlinear evolution equations (NLEEs) in mathematical physics and engineering. In this paper, the method is applied to construct exact solutions involving parameters for the foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions, the periodic wave and the rational function solutions are derived from exact solutions. These solutions might be imperative and significant for the explanation of some practical physical phenomena. It is shown that the method is an easy and advanced mathematical tool for solving NLEEs.