玻色-爱因斯坦凝聚体中观测到的怪波的非线性傅里叶光谱特征
Nonlinear Fourier spectral signatures of rogue waves observed in Bose-Einstein condensates
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中文总结 AI 辅助
本文采用非线性傅里叶变换研究玻色-爱因斯坦凝聚体中两类一阶怪波，揭示其非线性光谱机制，提出逆光谱工程方法，为理解控制该系统怪波形成提供新视角。
中文摘要 AI 辅助
调制不稳定性为理解连续背景上怪波（RW）的形成提供了重要框架，但具有消失边界条件的玻色-爱因斯坦凝聚体（BEC）物质波系统中怪波的形成机制和非线性光谱结构仍在很大程度上未被探索。本文中，我们基于聚焦非线性薛定谔方程的可积结构和Zakharov-Shabat散射问题，采用非线性傅里叶变换（NFT）研究BEC系统中两类代表性的一阶怪波。通过非线性光谱分析和达布变换重构，我们证明由高斯波包诱导的极端局域化事件以及实验观测到的 Peregrine孤子均受编码在非线性光谱中的离散孤子模的相干动力学支配。对于高斯初始态，增加初始宽度会导致离散本征值数量增加，从而发生从基态孤子和束缚态到圣诞树状怪波结构的转变；对于实验观测到的 Peregrine孤子，局域扰动会重塑离散光谱构型和相位演化，实现多个束缚孤子模的相干聚焦。此外，我们揭示了高阶怪波的光谱机制，并提出一种基于离散光谱相位匹配的逆光谱工程方法。我们的结果为理解和控制具有消失边界条件的物质波系统中的怪波形成提供了非线性光谱视角。
英文摘要
Modulation instability provides an important framework for understanding rogue wave (RW) formation on continuous backgrounds. However, the formation mechanism and nonlinear spectral structures of RWs in Bose-Einstein condensate (BEC) matter-wave systems with vanishing boundary conditions remain largely unexplored. Here, we employ the nonlinear Fourier transform (NFT), based on the integrable structure of the focusing nonlinear Schrödinger equation and the Zakharov-Shabat scattering problem, to investigate two representative classes of first-order RWs in BEC systems. Through nonlinear spectral analysis and Darboux reconstruction, we demonstrate that both Gaussian-wave-packet-induced extreme localization events and experimentally observed Peregrine solitons are governed by the coherent dynamics of discrete soliton modes encoded in the nonlinear spectrum. For Gaussian initial states, increasing the initial width leads to an increasing number of discrete eigenvalues, resulting in a transition from fundamental solitons and bound states to Christmas-tree-like RW structures. For experimentally observed Peregrine solitons, localized perturbations reshape the discrete spectral configuration and phase evolution, enabling coherent focusing of multiple bound soliton modes. Furthermore, we reveal the spectral mechanism of higher-order RWs and propose an inverse spectral-engineering approach based on discrete-spectrum phase matching. Our results provide a nonlinear spectral perspective for understanding and controlling RW formation in matter-wave systems with vanishing boundary conditions.
