Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

doi:10.1088/1674-1056/ad181e

中国物理B ›› 2024, Vol. 33 ›› Issue (3): 30502-030502.doi: 10.1088/1674-1056/ad181e

Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

Qian Zhang(张倩)¹, Xiankun Yao(姚献坤)^1,2,3,†, and Heng Dong(董恒)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:2023-10-16 修回日期:2023-12-18 接受日期:2023-12-22 出版日期:2024-02-22 发布日期:2024-02-29
通讯作者: Xiankun Yao E-mail:yaoxk@nwu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (NSFC) (Grant No. 12004309), the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSQ036), and the Scientific Research Program funded by Shaanxi Provincial Education Department (Grant No. 20JK0947).

Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

Qian Zhang(张倩)¹, Xiankun Yao(姚献坤)^1,2,3,†, and Heng Dong(董恒)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:2023-10-16 Revised:2023-12-18 Accepted:2023-12-22 Online:2024-02-22 Published:2024-02-29
Contact: Xiankun Yao E-mail:yaoxk@nwu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (NSFC) (Grant No. 12004309), the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSQ036), and the Scientific Research Program funded by Shaanxi Provincial Education Department (Grant No. 20JK0947).

摘要/Abstract

摘要： We show that the nonlinear stage of the dual-wavelength pumped modulation instability (MI) in nonlinear Schrödinger equation (NLSE) can be effectively analyzed by mode truncation methods. The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves. Significantly, the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure. It is demonstrated that there has much richer dynamic behavior, in contrast to the nonlinear waves reported before. This novel nonlinear wave promises to inject new vitality into the study of MI.

关键词: modulation instability, dual-wavelength pumps, latticed-Fermi-Pasta-Ulam recurrences

Abstract: We show that the nonlinear stage of the dual-wavelength pumped modulation instability (MI) in nonlinear Schrödinger equation (NLSE) can be effectively analyzed by mode truncation methods. The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves. Significantly, the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure. It is demonstrated that there has much richer dynamic behavior, in contrast to the nonlinear waves reported before. This novel nonlinear wave promises to inject new vitality into the study of MI.

Key words: modulation instability, dual-wavelength pumps, latticed-Fermi-Pasta-Ulam recurrences

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

52.35.Mw (Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.))

Qian Zhang(张倩), Xiankun Yao(姚献坤), and Heng Dong(董恒). Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation[J]. 中国物理B, 2024, 33(3): 30502-030502.

Qian Zhang(张倩), Xiankun Yao(姚献坤), and Heng Dong(董恒). Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation[J]. Chin. Phys. B, 2024, 33(3): 30502-030502.

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Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

Dual-wavelength pumped latticed Fermi-Pasta-Ulam recurrences in nonlinear Schrödinger equation

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