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.
Bibliographical note© 2014 American Physical Society
Funding: EPSRC (Project UNLOC) and a grant from the Ministry of Education and Science of the Russian Federation (Agreement No. 14.B25.31.0003).