Correspondence between the NLS equation for optical fibers and a class   of integrable NLS equations
  The propagation of the optical field complex envelope in a single-mode fiber is governed by a one-dimensional cubic nonlinear Schr\"odinger equation with a loss term. We present a result about $L^2$-closeness of the solutions of the above-mentioned equation and of a one-dimensional nonlinear Schr\"odinger equation that is Painlev\'e integrable. 
Domenico Felice and Luigi Barletti
math-ph math.MP