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Nth order generalized Darboux transformation and solitons, breathers and rogue waves in a variable-coefficient coupled nonlinear Schrödinger equation

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Abstract

Based on the generalized Darboux transformation, the underlying propagation mechanism of localized waves is systematically studied. More specifically, the variable-coefficient coupled nonlinear Schrödinger (NLS) equation is used to accurately describe the dispersion compensation and lumped amplification properties in an inhomogeneous optical fiber. Based on the Lax pair and the seed solutions, the expressions of both the first- and second-order localized wave solutions are calculated. Then, by performing numerical simulations, the evolutionary plots of the interaction of rogue waves with bright-dark solitons and breathers are obtained, and their dynamical characteristics are further analyzed. From the acquired results, it is found that the values of \(\beta \left( z \right) \) and \(\gamma \left( z \right) \) have a direct influence on the propagation shape of the localized waves. Our work provides valuable insights into the dynamical characteristics of the localized waves that the variable-coefficient equations could describe to a certain extent.

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Funding

The authors sincerely thanks for the support of the National Natural Science Foundation of China (NNSFC) through grant Nos. 11602232, Shanxi Natural Science Foundation (SNSF) through grant Nos. 202203021211086 and Nos. 202203021211088 and Shanxi Province Research Funding Program for Returning Students (2022-150).

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Authors and Affiliations

  1. Department of Mathematics, North University of China, Taiyuan, 030051, Shanxi, China

    N. Song, R. Liu & M. M. Guo

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    W. X. Ma

  3. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    W. X. Ma

  4. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    W. X. Ma

  5. School of Mathematical and Statistical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    W. X. Ma

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  1. N. Song
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  2. R. Liu
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Correspondence to N. Song or W. X. Ma.

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Song, N., Liu, R., Guo, M.M. et al. Nth order generalized Darboux transformation and solitons, breathers and rogue waves in a variable-coefficient coupled nonlinear Schrödinger equation. Nonlinear Dyn 111, 19347–19357 (2023). https://doi.org/10.1007/s11071-023-08843-7

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  • DOI: https://doi.org/10.1007/s11071-023-08843-7

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