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Modulation Instability Continuous Wave Nls Dark

Written By Saturday 15 October 2022 Add Comment Edit

Abstract

In this paper, rogue wave solutions of a sixth-order focusing nonlinear Schrödinger (NLS) equation with variable coefficients are investigated on a periodic background. To get the results, we take advantage of Darboux transformation approach and the nonlinearization of spectral problem and we firstly find one kind of rogue wave solution that evolves periodically with time on a periodically spatial background. Besides, we also find this kind of rogue wave solution dissipates over time. Modulation instability (MI) of the sixth-order focusing NLS equation with variable coefficients is also studied.

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The authors declare that all data supporting the findings of this study are available within the article.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11861050, 11261037), the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2020LH01010) and the Inner Mongolia Normal University Graduate Students' Research and Innovation Fund (Grant No. CXJJS21119).

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Authors and Affiliations

  1. Center for Applied Mathematical Science, Inner Mongolia, Hohhot, 010022, People's Republic of China

    Wei Shi &  Zhaqilao

  2. College of Mathematics Science, Inner Mongolia Normal University, Hohhot, 010022, People's Republic of China

    Wei Shi &  Zhaqilao

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Correspondence to Zhaqilao.

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Shi, W., Zhaqilao Modulation instability and rogue waves for the sixth-order nonlinear Schrödinger equation with variable coefficients on a periodic background. Nonlinear Dyn 109, 2979–2995 (2022). https://doi.org/10.1007/s11071-022-07538-9

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  • DOI : https://doi.org/10.1007/s11071-022-07538-9

Keywords

  • Rogue wave on a periodic background
  • Sixth-order focusing nonlinear Schrödinger equation
  • Variable coefficient
  • Modulation instability

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