Correspondence between the NLS equation for optical fibers and a class of integrable NLS equations

摘要

The propagation of the optical field complex envelope in a single-mode fiberis governed by a one-dimensional cubic nonlinear Schr\"odinger equation with aloss term. We present a result about $L^2$-closeness of the solutions of theabove-mentioned equation and of a one-dimensional nonlinear Schr\"odingerequation that is Painlev\'e integrable.