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The interaction of three long shallow-water waves with different dispersion relations modeled by generalized Hirota–Satsuma KdV systems with some variable coefficients

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Abstract

In this study, the generalized Hirota–Satsuma KdV systems with with some variable coefficients is used to simulate the interaction of three long waves in shallow water with different dispersion relations. Exact solutions of the equations under consideration are generated using a Lie symmetry transform and rapidly convergent approximation method. In terms of exponential functions, three new sets of exact solutions have been discovered. The solutions of the partial differential equations in question are then deduced by inverting them into the Lie symmetry transformation. A theorem has been put forth and proven to ensure that the first set of solutions obtained are bounded. The solutions are plotted using the results obtained from the theorems. The graphs show solutions that have different characteristics of multi-hump solutions. For different values of the arbitrary velocity function, the solution is shown to have M-shaped, S-shaped, L-shaped, snake-shaped, boomerang-shaped and boomerang-shaped with cyclic effects multi-hump soliton solutions. We find that by varying the variable coefficient, we can tune the structure of the above solitons. These results demonstrate not only the efficiency of the updated method, but also that the solution has been enhanced with new multi-hump features.

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Acknowledgements

The author appreciates the referees’ comments, which helped to improve the manuscript. The author acknowledges Professor Madan Mohan Panja of the mathematics department of Visva-Bharati for his helpful advice in revising the article.

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  1. Department of Mathematics, Triveni Devi Bhalotia College, Raniganj, West Bengal, 713347, India

    Prakash Kumar Das

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Das, P.K. The interaction of three long shallow-water waves with different dispersion relations modeled by generalized Hirota–Satsuma KdV systems with some variable coefficients. Nonlinear Dyn 111, 21259–21278 (2023). https://doi.org/10.1007/s11071-023-08929-2

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