Some results on discrete eigenvalues for the Stochastic Nonlinear Schroedinger Equation in fiber optics

TL;DR

This paper investigates the behavior of discrete eigenvalues in a stochastic nonlinear Schrödinger equation relevant to fiber optics, using perturbation methods to analyze the impact of noise on the nonlinear Fourier spectrum.

Contribution

It introduces a perturbation approach to study the statistics of discrete eigenvalues in a stochastic NLSE, advancing understanding of noise effects in nonlinear Fourier-based optical communication.

Findings

First-order perturbation describes eigenvalue statistics under noise.

The approach helps characterize channel properties in nonlinear Fourier communication.

Results aid in designing robust optical transmission systems.

Abstract

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.