AI 中文总结
研究两流体半空间界面处艾哈迈德iev呼吸子，基于奈菲模型结合参数映射与物理重构，构建参数映射并分析其综合作用，建立定量关系，分析不同区域代表性状态，为呼吸子研究提供新方法并可扩展应用。
AI 中文摘要
基于奈菲模型，开发了一种结合两流体半空间界面处艾哈迈德iev呼吸子参数映射和物理重构的方法。构建参数映射以表征呼吸子调制周期、调制不稳定性增长率以及束缚二次谐波对重构界面轮廓的相对贡献。其综合分析提供了超越非线性薛定谔方程传统聚焦条件的呼吸子状态的物理意义分类。物理界面轮廓的重构建立了非线性波变形与束缚二次谐波贡献之间的定量关系，从而能够确定弱非线性近似的适用范围。分析了来自不同调制不稳定性区域的代表性状态，以展示共振和聚焦边界对呼吸子特性和界面波轮廓的影响。所提出的方法在艾哈迈德iev呼吸子的数学描述与其物理解释之间提供了直接联系，并且可以扩展到非线性薛定谔方程的其他局部解以及广泛的分层流体动力学系统。
英文摘要
A methodology combining parameter mapping and physical reconstruction of Akhmediev breathers at the interface between two fluid half-spaces is developed on the basis of the Nayfeh model. Parameter maps are constructed to characterize the breather modulation period, the modulational instability growth rate, and the relative contribution of the bound second harmonic to the reconstructed interfacial profile. Their combined analysis provides a physically meaningful classification of breather regimes beyond the conventional focusing condition of the nonlinear Schrödinger equation. Reconstruction of the physical interfacial profile establishes a quantitative relation between nonlinear wave deformation and the contribution of the bound second harmonic, making it possible to identify the range of applicability of the weakly nonlinear approximation. Representative regimes from different modulational instability regions are analyzed to demonstrate the influence of resonance and focusing boundaries on breather characteristics and interfacial wave profiles. The proposed approach provides a direct link between the mathematical description of Akhmediev breathers and their physical interpretation and can be extended to other localized solutions of the nonlinear Schrödinger equation and to a broad class of stratified hydrodynamic systems.
Comments25 pages, 13 figures
