论文标题
带有噪声的盒形波场中的孤子：扰动理论和统计
Solitons in a box-shaped wavefield with noise: perturbation theory and statistics
论文作者
论文摘要
我们研究了非线性波场散射数据校正的基本问题，以响应使用逆散射变换理论的初始条件扰动。我们提出了一个完整的理论线性扰动框架，以评估可集成的一维焦点非线性schrödinger（NLSE）方程中整个散射数据的一阶校正。一般的散射数据肖像揭示了非线性相干结构 - 孤子 - 在波场演化中起关键作用。将开发的理论应用于经典的盒形波场，我们通过分析地求解了派生的方程式，以作为对初始条件的单个傅立叶模式的扰动，从而导致对基本孤子特征的灵敏度闭合形式表达式，即振幅，速度，速度，相位及其位置。通过适当的统计平均，我们对孤子噪声诱导的效应进行建模，从而导致孤子参数的标准偏差的紧凑关系。依靠虚拟孤子特征值的概念，我们得出了索尼族出现的概率或由于噪声而导致的相反，并通过NLSE进化的直接数值模拟说明了这些理论预测。提出的框架可以推广到其他可集成的系统和波场模式。
We investigate the fundamental problem of the nonlinear wavefield scattering data corrections in response to a perturbation of initial condition using inverse scattering transform theory. We present a complete theoretical linear perturbation framework to evaluate first-order corrections of the full set of the scattering data within the integrable one-dimensional focusing nonlinear Schrödinger (NLSE) equation. The general scattering data portrait reveals nonlinear coherent structures - solitons - playing the key role in the wavefield evolution. Applying the developed theory to a classic box-shaped wavefield we solve the derived equations analytically for a single Fourier mode acting as a perturbation to the initial condition, thus, leading to the sensitivity closed-form expressions for basic soliton characteristics, i.e. the amplitude, velocity, phase and its position. With the appropriate statistical averaging we model the soliton noise-induced effects resulting in compact relations for standard deviations of soliton parameters. Relying on a concept of a virtual soliton eigenvalue we derive the probability of a soliton emergence or the opposite due to noise and illustrate these theoretical predictions with direct numerical simulations of the NLSE evolution. The presented framework can be generalised to other integrable systems and wavefield patterns.
