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Travelling-wave, Mixed-lump-kink and Mixed-rogue-wave-kink Solutions for an Extended (3+1)-dimensional Shallow Water Wave Equation in Oceanography and Atmospheric Science

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Abstract

Shallow water waves are seen in oceanography, atmospheric science, and other fields. In this paper, we investigate an extended (3+1)-dimensional shallow water wave equation. We get the travelling-wave solutions via the polynomial-expansion method. Applying the Hirota method and symbolic computation, we derive some mixed-lump-kink and mixed-rogue-wave-kink solutions. Based on the mixed-lump-kink solutions, we graphically show the interaction between a lump and a kink soliton, and find two different cases: (1) the lump merges into the kink soliton; (2) the lump separates from the kink soliton. Based on the mixed-rogue-wave-kink solutions, we graphically analyze the interaction between the rogue wave and two-kink solitons, and find that the rogue wave emerges from the one kink soliton and merges into the other kink soliton.

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023 and 11471050, by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05) and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02.

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Shu-Jun Meng, Bo Tian, Shao-Hua Liu & Xiao-Tian Gao

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Shu-Jun Meng, Bo Tian, Shao-Hua Liu and Xiao-Tian Gao wrote the main manuscript text and Shu-Jun Meng prepared figures. All authors reviewed the manuscript.

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Correspondence to Bo Tian.

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Meng, SJ., Tian, B., Liu, SH. et al. Travelling-wave, Mixed-lump-kink and Mixed-rogue-wave-kink Solutions for an Extended (3+1)-dimensional Shallow Water Wave Equation in Oceanography and Atmospheric Science. Int J Theor Phys 63, 25 (2024). https://doi.org/10.1007/s10773-023-05477-8

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