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Soliton Propagation in Optical Fibers with Random Parameters

  • D. Gurarie
  • P. Mishnayevskiy
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 11)

Abstract

We study a system of nonlinear Schrödinger equations that models propagation of optical pulses in a monomode fiber. It includes linear terms (second and third order dispersions, and attenuation) as well as nonlinear terms (cross-phase modulation,and Raman scattering). The Whitham variational (averaging) method is used to reduce the nonlinear partial differential equations to an ordinary differential system for a finite number of soliton parameters: distance between pulses, phase frequency, width and amplitude. When the random medium coefficients are turned on the reduced ODE’s becomes a stochastic system. We derive the corresponding Fokker-Planck equation and discuss its solutions in special cases. The stationary Fokker-Planck solution (equilibrium ensemble) gives the expected mean values and correlations of soliton parameters over large spatial scales and allows us to analyze the long-term effects of the random fiber on the 2-pulse system.

Keywords

Optical Pulse Hamiltonian Structure Stationary Random Process Nonlinear Schrodinger Equation Order Dispersion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • D. Gurarie
  • P. Mishnayevskiy

There are no affiliations available

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