研究目的
To show that modulational instability can be used to explain the structure of breathers and rogue waves quantitatively, derive general forms for Akhmediev breathers, rogue waves, and their multiple or high-order ones in N-component nonlinear Schr?dinger equations, and clarify the existence conditions and consistency with linear stability analysis.
研究成果
The research establishes a quantitative relationship between modulational instability and homoclinic orbit solutions (Akhmediev breathers and rogue waves) in the VNLSE. It provides general solution formulas and shows that the dispersion relation from linear stability analysis determines the structures of these solutions. The findings enhance understanding of nonlinear excitations in various physical contexts, with potential applications in optics, Bose-Einstein condensates, and other fields.
研究不足
The study is theoretical and focuses on integrable systems like the VNLSE, which may not fully capture non-integrable or real-world physical systems. Numerical tests are limited to specific parameter sets, and the complexity increases with higher component numbers, making explicit solutions difficult to obtain.
