The Benney-Luke equation has contributed to studying the propagation of the water wave surfaces. This paper illustrates the (G’/G,1/G)-method to obtain the solutions of the Benney-Luke equation and an extension of the Benney-Luke equation. The new types of solutions are also constructed to gather the performance and visualization in three dimensions for observing the behaviors. The solutions are found in the expressions of hyperbolic functions giving the general performance by selecting arbitrary constants.
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Tuan et al. (2024) studied this question.
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