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Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

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  • Singh, Sudhir
  • Sakkaravarthi, K.
  • Murugesan, K.

Abstract

Physics of nonlinear waves on variable backgrounds and the relevant mathematical analysis continues to be the challenging aspect of the study. In this work, we consider a (3+1)-dimensional nonlinear model describing the dynamics of water waves and construct nonlinear wave solutions on spatio-temporally controllable backgrounds for the first time by using a simple mathematical tool auto-Bäcklund transformation. Mainly, we unravel physically interesting features to control and manipulate the dynamics of nonlinear waves through the background. Adapting an exponential function and general polynomial of degree two as initial seed solutions, we construct single kink-soliton and rogue wave, respectively. We choose arbitrary periodic, localized and combined wave backgrounds by incorporating Jacobi elliptic functions and investigate the modulation of these two nonlinear waves with a clear analysis and graphical demonstrations. The solutions derived in this work give us sufficient freedom to generate exotic nonlinear coherent structures on variable backgrounds and open up an interesting direction to explore the dynamics of various other nonlinear waves propagating through inhomogeneous media.

Suggested Citation

  • Singh, Sudhir & Sakkaravarthi, K. & Murugesan, K., 2022. "Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010067
    DOI: 10.1016/j.chaos.2021.111652
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    References listed on IDEAS

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    1. Du, Xia-Xia & Tian, Bo & Qu, Qi-Xing & Yuan, Yu-Qiang & Zhao, Xue-Hui, 2020. "Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2020. "Shallow water in an open sea or a wide channel: Auto- and non-auto-Bäcklund transformations with solitons for a generalized (2+1)-dimensional dispersive long-wave system," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Ding, Cui-Cui & Gao, Yi-Tian & Li, Liu-Qing, 2019. "Breathers and rogue waves on the periodic background for the Gerdjikov-Ivanov equation for the Alfvén waves in an astrophysical plasma," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 259-265.
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    1. Singh, Sudhir & Sakkaravarthi, K. & Murugesan, K., 2023. "Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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