<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study a stochastic Nonlinear Schrödinger 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. </p></abstract>

We study a stochastic Nonlinear Schrödinger 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.

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

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

We study a stochastic Nonlinear Schrödinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In...

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

Published Online: Mar 24, 2018

Page range: 87 - 103

Received: Jan 30, 2017

Accepted: Feb 20, 2018

DOI: https://doi.org/10.1515/caim-2015-0006

Keywords
Stochastic Nonlinear Schrödinger Equation, Nonlinear Fourier Transform, Eigenvalues, Solitons, Perturbation, Fiber Optics

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Mar 24, 2018

Page range: 87 - 103

Received: Jan 30, 2017

Accepted: Feb 20, 2018

DOI: https://doi.org/10.1515/caim-2015-0006

KeywordsStochastic Nonlinear Schrödinger Equation, Nonlinear Fourier Transform, Eigenvalues, Solitons, Perturbation, Fiber Optics

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Stochastic Nonlinear Schrödinger Equation, Nonlinear Fourier Transform, Eigenvalues, Solitons, Perturbation, Fiber Optics