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The deformed modified Korteweg–de Vries equation: Multi-soliton solutions and their interactions

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Abstract

In this paper, we demonstrate how Hirota’s bilinear method can be employed to derive single-soliton, two-soliton and three-soliton solutions of the deformed modified Korteweg–de Vries (KdV) equation. We note that the derived soliton solutions depend on the time-dependent function, revealing that the speed of the soliton solutions no longer explicitly depends on wave amplitude. Finally, we graphically demonstrate the evolution of multi-soliton solutions and their interactions.

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Acknowledgements

The author would like to thank the Management and Principal of C. Abdul Hakeem College (Autonomous), Melvisharam, Ranipet District, Tamil Nadu, India, for their support and encouragement.

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  1. PG and Reserarch Department of Mathematics, C. Abdul Hakeem College (Autonomous) (Affiliated to Thiruvalluvar University, Vellore), Hakeem Nagar, Melvisharam, Ranipet District, 632 509, India

    S Suresh Kumar

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Kumar, S.S. The deformed modified Korteweg–de Vries equation: Multi-soliton solutions and their interactions. Pramana - J Phys 97, 110 (2023). https://doi.org/10.1007/s12043-023-02581-6

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