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The modified simple equation method, the exp-function method, and the method of soliton ansatz for solving nonlinear partial differential equations are presented. Based on these three different methods, we obtain the exact solutions and the bright–dark soliton solutions with parameters of the long-short wave resonance equations which describe the resonance interaction between the long wave and the short wave. When these parameters take special values, the solitary wave solutions are derived from the exact solutions. We compare the results obtained using the three methods. Also, a comparison between our results and the well-known results is given.

The Modified Simple Equation Method, the Exp-Function Method, and the Method of Soliton Ansatz for Solving the Long–Short Wave Resonance Equations