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The distortion study of rogue waves of the generalized nonlinear Schrödinger equation under the third-order dispersion perturbation

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Abstract

We have investigated the robustness of the rogue wave solutions of two reductions of the generalized nonlinear Schrödinger equation with the third-order dispersion perturbation term. The two reductions are the nonlinear Schrödinger (NLS) equation and the second-type derivative nonlinear Schrödinger (DNLSII) equation. The perturbed equations have practical physical application value. However, they are non-integrable so their exact rogue wave solutions can hardly be obtained by analytical methods. In this paper, we use numerical methods to simulate the perturbed rogue wave solutions and use the quantitative analysis method to assess the robustness of the rogue wave solutions. Two criteria c and r are defined based on the definition of rogue waves in ocean science to analyze the distortion degree of rogue waves quantitatively. The numerical simulation results and the values of these criteria show that the rogue wave solutions of these two reductions are robust under the third-order dispersion perturbation, while the rogue wave solution of the DNLSII equation is more sensitive to the perturbation than that of the NLS equation.

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Funding

The work was supported by the National Natural Science Foundation of China (Grant Number 12071304), the Shenzhen Natural Science Fund(the Stable Support Plan Program) (Grant Number 20220809163103001).

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Authors and Affiliations

  1. Institute for Advanced Study, Shenzhen University, Shenzhen, 518060, Guangdong, People’s Republic of China

    Jingli Wang & Jingsong He

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  1. Jingli Wang
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  2. Jingsong He
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All authors contributed to the study conception and design. Analysis, review and editing were performed by Jingli Wang and Jingsong He. Numerical simulation was performed by Jingli Wang. The first draft of the manuscript was written by Jingli Wang, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Jingsong He.

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Wang, J., He, J. The distortion study of rogue waves of the generalized nonlinear Schrödinger equation under the third-order dispersion perturbation. Nonlinear Dyn 111, 17473–17482 (2023). https://doi.org/10.1007/s11071-023-08763-6

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