Conditional probability calculations for the nonlinear Schrödinger equation with additive noise

The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly no...

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Bibliographic Details
Published in:Physical review letters 2014-12, Vol.113 (23), p.230602-230602, Article 230602
Main Authors: Terekhov, I S, Vergeles, S S, Turitsyn, S K
Format: Article
Language:English
Subjects:
Additives
Conditional probability
Density
Mathematical analysis
Mathematical models
Models, Theoretical
Noise
Nonlinear Dynamics
Nonlinearity
Probability
Quantum Theory
Schroedinger equation
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Summary:The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.113.230602