中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30506-030506.doi: 10.1088/1674-1056/ad11e7

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Parametric instability in the pure-quartic nonlinear Schrödinger equation

Yun-Hong Zhang(张云红)1,2 and Chong Liu(刘冲)1,2,3,†   

  1. 1 School of Physics, Northwest University, Xi'an 710127, China;
    2 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China;
    3 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
  • 收稿日期:2023-10-20 修回日期:2023-11-28 接受日期:2023-12-04 出版日期:2024-02-22 发布日期:2024-03-06
  • 通讯作者: Chong Liu E-mail:chongliu@nwu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12175178 and 12247103), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2022KJXX-71), and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY016).

Parametric instability in the pure-quartic nonlinear Schrödinger equation

Yun-Hong Zhang(张云红)1,2 and Chong Liu(刘冲)1,2,3,†   

  1. 1 School of Physics, Northwest University, Xi'an 710127, China;
    2 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Xi'an 710127, China;
    3 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China
  • Received:2023-10-20 Revised:2023-11-28 Accepted:2023-12-04 Online:2024-02-22 Published:2024-03-06
  • Contact: Chong Liu E-mail:chongliu@nwu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 12175178 and 12247103), the Natural Science Basic Research Program of Shaanxi Province, China (Grant No. 2022KJXX-71), and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY016).

摘要: We study the nonlinear stage of modulation instability (MI) in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically. Using the three-mode truncation, we reveal the complex recurrence of parametric resonance (PR) breathers, where each recurrence is associated with two oscillation periods (PR period and internal oscillation period). The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

关键词: modulation instability, parametric resonance breather, three-mode truncation, energy exchange

Abstract: We study the nonlinear stage of modulation instability (MI) in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically. Using the three-mode truncation, we reveal the complex recurrence of parametric resonance (PR) breathers, where each recurrence is associated with two oscillation periods (PR period and internal oscillation period). The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.

Key words: modulation instability, parametric resonance breather, three-mode truncation, energy exchange

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.10.-a (Computational methods in statistical physics and nonlinear dynamics)