In this work, by implementing the generalized -expansion method, we present exact solutions of a completely integrable model namely; Whitham-Broer-Kaup (WBK) equations. The considered equation describes the small amplitude regime for dispersive long waves in shallow water. The solutions are obtained in terms of exponential functions, trigonometric functions and rational functions. Moreover, by selecting arbitrary constants appropriately in the solutions, we discovered various interesting periodic soliton structures. Also, innovative as well as distinct exact solutions raised in this paper may hold powerful applications in various fields of mathematical physics.
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