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N-soliton Solutions and Nonlinear Dynamics for a Generalized Broer–Kaup System

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Computational and Experimental Simulations in Engineering (ICCES 2023)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 143))

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Abstract

Water waves are observed in many situations, as well as on rivers, lakes or oceans. Under consideration in this paper is a famous dispersion water wave model: the (1 + 1)-dimensional generalized Broer–Kaup (gBK) system. This system is used to simulate the bi-directional propagation of long waves in shallow water. Based on the bilinear forms given in this paper, novel N-soliton solutions of this gBK system is obtained by using Hirota's bilinear method. In order to understand the nonlinear dynamics localized in the gBK systems, local structures of the obtained one-, two-, three- and four-soliton solutions are shown. This paper reveals the local structures of the one-soliton solutions and interactions between multi-soliton solutions and preliminarily explains the nonlinear dynamical characteristics of bell soliton and kink soliton in this gBK system.

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11805020, 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, Beijing, 100876, China

    Tian-zhi Liu & Yan Jiang

  2. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Tian-zhi Liu, Yan Jiang, Yan Jiang, Tian Bo & Fan Bai

Authors
  1. Tian-zhi Liu
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  2. Yan Jiang
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  3. Tian Bo
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  4. Fan Bai
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Corresponding author

Correspondence to Yan Jiang .

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Editors and Affiliations

  1. Dept of Civil and Env'l Engg, University of California, Berkeley, Berkeley, CA, USA

    Shaofan Li

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Liu, Tz., Jiang, Y., Bo, T., Bai, F. (2024). N-soliton Solutions and Nonlinear Dynamics for a Generalized Broer–Kaup System. In: Li, S. (eds) Computational and Experimental Simulations in Engineering. ICCES 2023. Mechanisms and Machine Science, vol 143. Springer, Cham. https://doi.org/10.1007/978-3-031-42515-8_32

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  • DOI: https://doi.org/10.1007/978-3-031-42515-8_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-42514-1

  • Online ISBN: 978-3-031-42515-8

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