Abstract
The Jacobi elliptic function expansion method is one of the most powerful tools for exploring exact solutions of nonlinear partial differential models, which is used in this work to characterize the interaction between one long longitudinal wave and one short transverse wave propagation in a generalized elastic medium. First, we applied a wave transform to the proposed system of equations and obtained an ordinary differential equation. We obtain the values of involved free parameters after performing necessary operations, then substitute the obtained values to the ordinary differential equation by considering the constructed solutions to the ordinary and then to the partial differential equation. As a result, different structures of solutions are constructed such as solitary dark–bright, dark, bright, singular, trigonometric function, Jacobi elliptic function, and hyperbolic function solutions. In order to illustrate the tsunami and tidal oscillations, we draw 3D surfaces and 2D graphics for the obtained solutions by giving a specific value for the involved parameters under the given conditions.
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