AI 中文总结
研究基于孤子特征值响应函数及逆问题，开发操纵和重构 sech 形非线性波场的理论框架，推导微扰表达式与传感概念，介绍逆问题积分方程，评估重构机制并证明噪声下可靠解，迈向孤子层析成像。
AI 中文摘要
不同物理性质的非线性脉冲的孤子含量普遍由一组离散的特征值表征。在由非线性薛定谔方程支配的理想信道中，特征值沿波场传播不变。微扰会在特征值图谱上留下可预测的印记，近期已用于操纵光纤孤子。本文基于孤子特征值响应函数及相应逆问题，开发了一个操纵和重构 sech 形非线性波场的理论框架。推导了通过施加即时、可控微扰实现孤子非线性操纵的解析表达式，提出了微扰传感概念，介绍了用于重构未知波场畸变形状逆问题的积分方程，评估了不同重构机制并证明了在噪声存在下可靠的逆问题解决方案，为孤子层析成像铺平了道路。
英文摘要
Soliton content of nonlinear pulses of different physical nature is universally characterized by a discrete set of eigenvalues. In an ideal channel governed by the nonlinear Schrodinger equation, the eigenvalues do not change along the wave field propagation. Perturbations leave predictable fingerprints on the eigenvalue portrait, which was recently used to manipulate optical fiber solitons in [Phys. Rev. Lett. 134, 193804, 2025]. Here, we develop a theoretical framework to manipulate and reconstruct sech-shaped nonlinear wave fields based on soliton eigenvalue response functions and the corresponding inverse problem. We derive analytical expressions to enable nonlinear manipulation of solitons by applying instant, controllable perturbations. Then we present a concept of perturbation sensing with the key feature of nonlinear propagation of the probe signal over an unknown distance, enabling the extraction of information about the perturbation source hidden within nonlinear media or materials. We introduce an integral equation for the inverse problem of reconstructing the unknown shape of the wave field distortions, when the known observational data is a function of deviations in soliton eigenvalues measured at the end of the nonlinear propagation channel. We evaluate different reconstruction regimes and demonstrate a reliable inverse problem solution in presence of noise, paving the way towards soliton tomography.
Comments10 pages, 9 figures
