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Novel localized waves and interaction solutions for a dimensionally reduced (2 + 1)-dimensional Boussinesq equation from N-soliton solutions

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Abstract

The Boussinesq equation has been of considerable interest in coastal and ocean engineering models for simulating surface water waves in shallow seas and harbors, tsunami wave propagation, wave overtopping, inundation, and near-shore wave process. Consequently, the study deals with the dynamics of localized waves and interaction solutions to a dimensionally reduced (2 + 1)-dimensional Boussinesq equation from N-soliton solutions by Hirota’s bilinear method. The integrability of the equation of interest was confirmed via the Painlevé test. Taking the long-wave limit approach in coordination with some constraint parameters available in the N-soliton solutions, the localized waves and interaction solutions are constructed. The interaction solutions can be obtained among the localized waves, such as (1) one breather or one lump from the two solitons, (2) one stripe and one breather, and one stripe and one lump from the three solitons, and (3) two stripes and one breather, one lump and one periodic breather, two stripes and one lump, two breathers, and two lumps from the four solitons. The interactions among the solitons are found to be elastic. The energy, phase shift, shape, period, amplitude, and propagation direction of each of the localized waves and interaction solutions are found to be influenced and controlled by the parameters involved. The dynamical characteristics of these localized waves and interaction solutions are demonstrated through some 3D and density graphs. The outcomes achieved in this study can be used to illustrate the wave interaction phenomena in shallow water.

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Data availability statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors are grateful to three anonymous referees for a number of helpful and perceptive comments for improving the manuscript. This work was partially supported by a grant from the University Grants Commission, Bangladesh, through the Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj (3632104), and the National Science and Technology (NST), Government of Bangladesh, by providing NST fellowship (39.00.0000.012.002.04.19-06). The first and second authors acknowledge this support, respectively.

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Authors and Affiliations

  1. Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj, 8100, Bangladesh

    Dipankar Kumar & Md. Nuruzzaman

  2. Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh

    Gour Chandra Paul & Ashabul Hoque

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  1. Dipankar Kumar
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  2. Md. Nuruzzaman
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  4. Ashabul Hoque
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Contributions

Dipankar Kumar (conceptualization: lead; data curation: equal; formal analysis: lead; investigation: lead; methodology: equal; resources: equal; software: equal; supervision: equal; validation: equal; writing—review and editing: equal). Md. Nuruzzaman (formal analysis: equal; funding acquisition: equal; methodology: equal; software: equal; writing—original draft: lead). Gour Chandra Paul (data curation: equal; formal analysis: equal; methodology: equal; resources: equal; software: equal; supervision: equal; validation: equal; writing—review and editing: equal). Ashabul Hoque (formal analysis: equal; supervision: equal; validation: equal; writing—review and editing: equal). Finally, all authors have approved this manuscript and take responsibility for the accuracy of its contents.

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Correspondence to Dipankar Kumar or Gour Chandra Paul.

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Kumar, D., Nuruzzaman, M., Paul, G.C. et al. Novel localized waves and interaction solutions for a dimensionally reduced (2 + 1)-dimensional Boussinesq equation from N-soliton solutions. Nonlinear Dyn 107, 2717–2743 (2022). https://doi.org/10.1007/s11071-021-07077-9

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