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Title: Propagation of ultra-short solitons in stochastic Maxwell's equations

We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase velocity, (c) the nonlinear coefficient. Using a modified multi-scale expansion for stochastic systems, we derive new stochastic generalizations of the short pulse equation that approximate the solutions of stochastic nonlinear Maxwell's equations. Numerical simulations show that soliton solutions of the short pulse equation propagate stably in stochastic nonlinear Maxwell's equations and that the generalized stochastic short pulse equations approximate the solutions to the stochastic Maxwell's equations over the distances under consideration. This holds for both a pathwise comparison of the stochastic equations as well as for a comparison of the resulting probability densities.
Authors:
 [1] ;  [2]
  1. Department of Science, Borough of Manhattan Community College, City University of New York, New York, New York 10007 (United States)
  2. Department of Mathematics, College of Staten Island, City University of New York, Staten Island, New York 10314 (United States)
Publication Date:
OSTI Identifier:
22251118
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTERIZED SIMULATION; MATHEMATICAL SOLUTIONS; MAXWELL EQUATIONS; NONLINEAR PROBLEMS; PHASE VELOCITY; SOLITONS; STOCHASTIC PROCESSES