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Related Experiment Video

Updated: Apr 19, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Conditional probability calculations for the nonlinear Schrödinger equation with additive noise.

I S Terekhov¹, S S Vergeles², S K Turitsyn³

¹Budker Institute of Nuclear Physics of SB RAS, Novosibirsk 630090, Russia and Novosibirsk State University, Novosibirsk 630090, Russia.

Physical Review Letters

|December 20, 2014

Summary

A new method computes the conditional probability density function for the nonlinear Schrödinger equation with noise. This approach is demonstrated for small noise limits and weakly nonlinear cases, with applications in fiber-optic communications.

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Published on: May 30, 2014

Area of Science:

Nonlinear optics
Stochastic processes
Computational mathematics

Background:

The nonlinear Schrödinger equation (NLSE) models wave propagation in various media.
Accurate computation of conditional probability density functions (CPDFs) is crucial for analyzing systems with noise.
Existing methods may struggle with the complexity of NLSE under noisy conditions.

Purpose of the Study:

Develop a novel method for calculating the CPDF for the NLSE with additive noise.
Provide a constructive form for the CPDF in the small noise limit.
Analytically derive the CPDF for weakly nonlinear scenarios.

Main Methods:

Development of a computational method for CPDF.
Analysis in the limit of small additive noise.
Analytical derivation for weakly nonlinear cases of the NLSE.

Main Results:

A constructive method for computing the CPDF of the NLSE with noise is presented.
The CPDF is derived analytically for small noise and weakly nonlinear regimes.
The theoretical results are validated using fiber-optic communication systems.

Conclusions:

The developed method offers a robust way to determine the CPDF for noisy NLSE.
The findings are particularly relevant for practical applications like optical communications.
This work advances the understanding and analysis of nonlinear systems with stochastic perturbations.