发表机构
School of Control and Computer Engineering, North China Electric Power University; School of Mathematics and Physics, North China Electric Power University（华北电力大学控制与计算机工程学院; 华北电力大学数理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究耦合Lakshmanan-Porsezian-Daniel方程中四阶效应诱导的矢量局域波状态跃迁，发现简并呼吸子可转化为孤子、拍频孤子仅在简并区可转化为稳定孤子，并推导了跃迁条件，数值模拟验证了精确解。
AI 中文摘要
我们研究了耦合Lakshmanan-Porsezian-Daniel方程中的新型矢量局域波解，该方程描述了海森堡铁磁自旋链的动力学。我们在简并区和非简并区分别给出了Tajiri-Watanabe呼吸子、怪波和共振模，以及简并拍频孤子。四阶效应在两个区域均诱导了状态跃迁。特别地，简并呼吸子可以转化为孤子，而这种跃迁在耦合Hirota方程中是不存在的。此外，拍频孤子仅在简并区可以转化为稳定孤子，这一现象在Manakov系统中未被发现。我们进一步揭示了共振模的状态跃迁，并推导了每个分支相应的跃迁条件。我们推导了物理谱，随后在谱域中确定了简并和非简并两种情况下的状态跃迁条件。这些谱为跃迁动力学提供了额外的表征。最后，我们进行了直接数值模拟以验证精确解的有效性。
英文摘要
We investigate novel vector localized wave solutions in the coupled Lakshmanan-Porsezian-Daniel equa?tions, which describe the dynamics of the Heisenberg ferromagnetic spin chain. We present Tajiri-Watanabe breathers, rogue waves and resonant modes in both the degenerate and non-degenerate regions, together with the degenerate beating solitons. The fourth-order effect induces state transitions in both regions. In particular, the degenerate breathers can be transformed into solitons, whereas such transitions are absent in the coupled Hirota equations. Moreover, beating solitons can be converted into stable solitons only in the degenerate region, the phenomena not found in the Manakov system. We further uncover the state transitions of the resonant modes and derive the corresponding transition conditions for each branch. We derive the physical spectra and subsequently identify the state transition conditions in the spectral domain for both the degenerate and non-degenerate cases. These spectra provide an additional characterization of the transition dynamics. Finally, direct numerical simulations are performed to verify the validity of the exact solutions.
