Noise bandwidth dependence of soliton phase in simulations of stochastic nonlinear SchrÄodinger equations

We demonstrate that soliton perturbation theory, though widely used, predicts an incorrect phase distribution for solitons of stochastically driven nonlinear SchrÄodinger equations in physically relevant parameter regimes. We propose a simple variational model that accounts for the e®ect of radiation on phase evolution and correctly predicts its distribution.