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A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized nonlinear evolution equation in plasmas

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Abstract

This paper proposes a new integrable generalized (3+1)-dimensional nonlinear partial differential equation. We apply the standard Painlevé test to check the integrability, which shows the complete integrability of this equation. We employ symbolic computation directly to create the rogue waves using the center-controlled parameters \(\beta \) and \(\gamma \). We create first-, second-, and third-order rogue wave solutions via direct computation for various values of center-controlled parameters and suitable choices of different constants in the said equation. We obtain the bilinear equation in the auxiliary function f of the transformed variables \(\xi \) and \(\eta \) by using the transformation for dependent variable u. Using Hirota’s direct method to create rogue waves up to the third order, we apply the generalized formula for rogue waves formulated by N-soliton. Using the symbolic system tool Mathematica, we illustrate the dynamics for the rogue wave solutions with various center-controlled parameters. We demonstrate how massive rogue waves, present in many nonlinear events, behave dominantly over tiny rogue waves. The equation investigates the development of long waves with small amplitudes traveling in plasma physics and wave motion in fluids and other weakly dispersive mediums. Scientific areas, including oceanography, fluid dynamics, dusty plasma, optical fibers, nonlinear dynamics, and numerous other nonlinear fields, show the occurrence of rogue waves in one way or another.

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Acknowledgements

The authors would like to thank the Editor and the referees for their insightful, encouraging, and helpful suggestions. Sachin Kumar, the author, would also like to express gratitude to the Science and Engineering Research Board (SERB), India, for financial support provided through the MATRICS Scheme (MTR/2020/000531).

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Authors and Affiliations

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

    Sachin Kumar

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

    Brij Mohan

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Kumar, S., Mohan, B. A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized nonlinear evolution equation in plasmas. Nonlinear Dyn 111, 16395–16405 (2023). https://doi.org/10.1007/s11071-023-08683-5

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