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Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model

Author

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

Abstract

The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of active research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model describing the evolution of water waves with higher-order temporal dispersion by characterizing the dynamics of lump and soliton waves on different spatially-varying backgrounds. Particularly, we construct some explicit lump wave and kink-soliton solutions for the considered model through its trilinear and bilinear equations with appropriate forms of the polynomial and exponential type initial seed solutions, respectively. Additionally, we obtain hyperbolic and periodic waves through bilinear Bäcklund transformation. We explore their propagation and transformation/modulation dynamics due to different spatial backgrounds through categorical analysis and clear graphical demonstrations for a complete understanding of the resulting solutions. Our analysis shows that the lump solution results into a simultaneous existence of well-localized spike and declining (coupled bright-dark wave) structures on a constant background, while the soliton solution exhibits kink and anti-kink wave patterns along different spatio-temporal domains with controllable properties. When the arbitrary spatial background is incorporated appropriately, we can witness the manifestation of soliton into manipulated periodic and interacting dynamical structures. On the other hand, the lump wave results into the coexistence, interacting wave and breather formation due to periodic and localized type arbitrary spatial backgrounds. The present results will be an important addition to the context of engineering nonlinear waves with non-vanishing controllable backgrounds in higher-dimensional models. Further, the present study can be extended to investigate several other nonlinear systems to understand the physical insights of the variable background in their dynamics.

Suggested Citation

  • 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).
  • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012371
    DOI: 10.1016/j.chaos.2022.113058
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    References listed on IDEAS

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    1. Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2022. "Taking into consideration an extended coupled (2+1)-dimensional Burgers system in oceanography, acoustics and hydrodynamics," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Zhenhao Zhang & Changchun Luo & Zhenpeng Zhao, 2020. "Application of probabilistic method in maximum tsunami height prediction considering stochastic seabed topography," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 104(3), pages 2511-2530, December.
    3. Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2022. "Regarding the shallow water in an ocean via a Whitham-Broer-Kaup-like system: hetero-Bäcklund transformations, bilinear forms and M solitons," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. 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).
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