2005/09/11 by S. A. Derevyanko, Stanislav Derevyanko, Jaroslaw E. Prilepsky +2 · 12 citations
Mathematics · Physics and Astronomy · #Adiabatic process #Advanced Fiber Laser Technologies #Amplitude #Fokker–Planck equation #Gaussian #Mathematics #Nonlinear system #Partial differential equation #Physics #Polarization (electrochemistry) #Probability density function #Quantum electrodynamics #Quantum mechanics #Soliton #Statistical Mechanics and Entropy #Statistical physics #Statistics #Theoretical and Computational Physics #White noise #nlin.CD #nlin.SI
paper · pdf · doi:10.1088/0305-4470/39/6/006
published in Journal of Physics A Mathematical and General 39(6), 1297-1309 (Institute of Physics) · Submitted to J.Phys.A: Mathematical and General
arxiv created 2005/09/11 · openalex publication_date 2006/01/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We investigate the statistics of a vector Manakov soliton in the presence of additive Gaussian white noise. The adiabatic perturbation theory for a Manakov soliton yields a stochastic Langevin system which we analyse via the corresponding Fokker–Planck equation for the probability density function (PDF) for the soliton parameters. We obtain marginal PDFs for the soliton frequency and amplitude as well as soliton amplitude and polarization angle. We also derive formulae for the variances of all soliton parameters and analyse their dependence on the initial values of polarization angle and phase.