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Generalised exponential rational function method for obtaining numerous exact soliton solutions to a (\(3+1\))-dimensional Jimbo–Miwa equation

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Abstract

In this work, we apply the generalised exponential rational function (GERF) method on an extended (\(3+1\))-dimensional Jimbo–Miwa (JM) equation which describes the modelling of water waves of long wavelength with weakly nonlinear restoring forces and frequency dispersion. This JM equation is also used to construct modelling waves in ferromagnetic media and two-dimensional matter-wave pulses in Bose–Einstein condensates. The main purpose is to construct analytical wave solutions for the (\(3+1\))-dimensional JM equation by utilising the GERF method with the help of symbolic computations. We have also presented three-dimensional plots to observe the dynamics of obtained results. To understand physical phenomenon through different shapes of solitary waves, we discussed solitons, the interaction of multiwave solitons, lump-type solitons and kink-type solutions.

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Acknowledgements

This work is funded by Science and Engineering Research Board (SERB), DST, India, under project scheme MATRICS via grant No. MTR/2020/000531. The author, Sachin Kumar, has received this research grant.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi, 110 007, India

    Sachin Kumar

  2. Department of Mathematics, SGTB Khalsa College, University of Delhi, Delhi, 110 007, India

    Dharmendra Kumar

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  1. Sachin Kumar
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  2. Dharmendra Kumar
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Correspondence to Dharmendra Kumar.

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Kumar, S., Kumar, D. Generalised exponential rational function method for obtaining numerous exact soliton solutions to a (\(3+1\))-dimensional Jimbo–Miwa equation. Pramana - J Phys 95, 152 (2021). https://doi.org/10.1007/s12043-021-02174-1

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  • DOI: https://doi.org/10.1007/s12043-021-02174-1

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