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Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in soliton theory and nonlinear waves

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Abstract

In soliton theory and nonlinear waves, this research proposes a new Painlevé integrable generalized (3+1)-D evolution equation. It demonstrates the Painlevé test that claims the integrability of the proposed equation and employs Cole–Hopf transformations to generate the trilinear equation in an auxiliary function that governs the higher-order rogue wave and dispersive-soliton solutions via the symbolic computation approach and dispersive-soliton assumption, respectively. Center-controlled parameters in rogue waves show the different dynamical structures with several other parameters. We obtain solutions for rogue waves up to third-order using direct symbolic analysis with appropriate center parameters and other parameters using a generalized procedure for rogue waves. We assume the dispersive-soliton solution, inspired by Hirota’s direct techniques to create dispersive-soliton solutions up to the third order. By applying the symbolic software Mathematica, we demonstrate the dynamical structures for rogue waves with diverse center parameters and dispersive solitons using dispersion relation to showcase the interaction behavior of the solitons. Dispersive solitons and rogue waves are fascinating phenomena that appear in diverse areas of physics, such as optical fibers, nonlinear waves, dusty plasma physics, nonlinear dynamics, and other engineering and sciences.

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Acknowledgements

The authors would like to express their appreciation to the Editor and the referees for their insightful and informative comments. The author, Sachin Kumar, wishes to acknowledge the Institution of Eminence, University of Delhi, India, for financial support in carrying out this research through the Faculty Research Programme Grant - IoE via Ref. No./IoE/2023-24/12/FRP.

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Authors and Affiliations

  1. Department of Mathematics, Hansraj College, University of Delhi, Delhi, 110007, India

    Brij Mohan

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110007, India

    Sachin Kumar

  3. Department of Mathematics, Kirorimal College, University of Delhi, Delhi, 110007, India

    Raj Kumar

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  1. Brij Mohan
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Correspondence to Sachin Kumar.

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Mohan, B., Kumar, S. & Kumar, R. Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in soliton theory and nonlinear waves. Nonlinear Dyn 111, 20275–20288 (2023). https://doi.org/10.1007/s11071-023-08938-1

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