论文标题
在光纤中的随机非线性Schr Oedinger方程的离散特征值的一些结果
Some results on discrete eigenvalues for the Stochastic Nonlinear Schroedinger Equation in fiber optics
论文作者
论文摘要
我们通过非线性傅立叶变换（NFT）研究了具有加性白色高斯噪声的随机非线性schroedinger方程（NLSE）。特别是，我们专注于沿聚焦纤维的离散特征值的传播。由于随机NLSE并非通过NFT完全集成，因此我们使用扰动方法，在该方法中，我们假设信噪比很高。零阶扰动导致确定性的NLSE，而一阶扰动允许描述离散特征值的统计数据。这对于了解最近设计的光传输技术的通道的性质很重要，该信息在非线性傅立叶频谱中编码。
We study a stochastic Nonlinear Schroedinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber. Since the stochastic NLSE is not exactly integrable by means of the NFT, then we use a perturbation approach, where we assume that the signal-to-noise ratio is high. The zeroth-order perturbation leads to the deterministic NLSE while the first-order perturbation allows to describe the statistics of the discrete eigenvalues. This is important to understand the properties of the channel for recently devised optical transmission techniques, where the information is encoded in the nonlinear Fourier spectrum.
