Diverging probabilitydensity functions for flattop solitary waves
Abstract
We investigate the statistics of flattop solitary wave parameters in the presence of weak multiplicative dissipative disorder. We consider first propagation of solitary waves of the cubicquintic nonlinear Schrödinger equation (CQNLSE) in the presence of disorder in the cubic nonlinear gain. We show by a perturbative analytic calculation and by Monte Carlo simulations that the probabilitydensity function (PDF) of the amplitude η exhibits loglognormal divergence near the maximum possible amplitude η_{m} , a behavior that is similar to the one observed earlier for disorder in the linear gain [A. Peleg , Phys. Rev. E 72, 027203 (2005)]. We relate the loglognormal divergence of the amplitude PDF to the superexponential approach of η to η_{m} in the corresponding deterministic model with linear/nonlinear gain. Furthermore, for solitary waves of the derivative CQNLSE with weak disorder in the linear gain both the amplitude and the group velocity β become random. We therefore study analytically and by Monte Carlo simulations the PDF of the parameter p , where p=η/(1ɛ_{s}β/2) and ɛ_{s} is the selfsteepening coefficient. Our analytic calculations and numerical simulations show that the PDF of p is loglognormally divergent near the maximum p value.
 Publication:

Physical Review E
 Pub Date:
 August 2009
 DOI:
 10.1103/PhysRevE.80.026602
 arXiv:
 arXiv:0906.3001
 Bibcode:
 2009PhRvE..80b6602P
 Keywords:

 05.45.Yv;
 05.40.a;
 47.54.r;
 42.65.Tg;
 Solitons;
 Fluctuation phenomena random processes noise and Brownian motion;
 Pattern selection;
 pattern formation;
 Optical solitons;
 nonlinear guided waves;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 9 pages, 6 figures. Submitted to Phys. Rev. E