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Controllable rogue waves on the Jacobi-periodic background for the higher-order nonlinear Schrödinger equation

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Abstract

Based on Darboux transformation and nonlinearization method, we construct rogue wave solutions of the higher-order nonlinear Schrödinger equation on two distinct Jacobi-periodic wave backgrounds, specifically, dnoidal and cnoidal waves. The distribution characteristics of the Lax spectrum for the Jacobi-periodic waves are shown at the \(\lambda \) complex plane. The effects of dispersion parameters \(\delta _2\) and \(\delta _6\), the elliptic modulus k, and the integral constants C and \(C_1\) on the dynamical behavior of rogue wave solutions under two different periodic wave backgrounds are systematically analyzed, and shown in detail through graphics. In particular, we find that the integral constant can achieve the controllable excitation of rogue waves at fixed points and the fission of higher-order rogue waves into rogue wave pairs, which exhibit some novel dynamical phenomena.

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Data availability statement

All data generated or analysed during this study are included in this published article.

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Acknowledgements

The authors would like to thank the referees for valuable comments and suggestions.

Funding

The funding was provided by the National Natural Science Foundation of China (Nos. 12301307, 12005027), Scientific Research Foundation of Chongqing Normal University (No. 23XLB023), Natural Science Foundation of Chongqing (Nos. CSTB2023NSCQ-MSX0053, CSTB2023NSCQ-MSX0501), Science and Technology Research Program of Chongqing Municipal Education Commission (Nos. KJQN202300554 and KJQN202300806) and Scientific Research Foundation of Chongqing Technology and Business University (No. 2156018).

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Lili Huang

  2. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Yunfei Yue

  3. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Yunfei Yue

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  1. Lili Huang
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  2. Yunfei Yue
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Contributions

Lili Huang (Conceptualization: Lead; Formal analysis: Lead; Investigation: Lead; Methodology: Lead; Resources: Lead; Software: Lead; Visualization: Lead; Funding acquisition: Lead; Writing–‘original draft: Lead; Writing’–review & editing: Equal) Yunfei Yue (Conceptualization: Supporting; Formal analysis: Supporting; Funding acquisition: Lead; Investigation: Supporting; Methodology: Supporting; Project administration: Equal; Writing‘–original draft: Supporting; Writing’–review -& editing: Equal).

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Correspondence to Yunfei Yue.

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Huang, L., Yue, Y. Controllable rogue waves on the Jacobi-periodic background for the higher-order nonlinear Schrödinger equation. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09858-4

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