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 het...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.展开更多
We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on t...We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on the frequency-wavenumber plane.Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate.展开更多
基金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)the Scientific Research Program funded by Shaanxi Provincial Education Department(Grant No.20JK0947).
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175178,12047502,and 12004309)the Major Basic Research Program of Natural Science of Shaanxi Province(Grant No.2017KCT-12)the Natural Science basic Research Program of Shaanxi Province(Grant No.2022KJXX-71)。
文摘We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on the frequency-wavenumber plane.Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate.
