Diverging probability density functions for flat-top solitary waves

Abstract

We investigate the statistics of flat-top solitary wave parameters in the presence of weak multiplicative dissipative disorder. We consider first propagation of solitary waves of the cubic-quintic 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 probability density function (PDF) of the amplitude $\eta$ exhibits loglognormal divergence near the maximum possible amplitude ${\eta }_m$, a behavior that is similar to the one observed earlier for disorder in the linear gain [A. Peleg et al., Phys. Rev. E {\bf 72}, 027203 (2005)]. We relate the loglognormal divergence of the amplitude PDF to the super-exponential approach of $\eta$ to ${\eta }_m$ 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 $\beta$ become random. We therefore study analytically and by Monte Carlo simulations the PDF of the parameter $p$, where $p=\eta /(1-{\epsilon }_s\beta /2)$ and ${\epsilon }_s$ is the self-steepening coefficient. Our analytic calculations and numerical simulations show that the PDF of $p$ is loglognormally divergent near the maximum $p$-value.

9 pages, 6 figures. Submitted to Phys. Rev. E

References in corpus (3)

• Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
• Monte Carlo simulations of pulse propagation in massive multichannel optical fiber communication systems
• Intermittent dynamics, strong correlations, and bit-error-rate in multichannel optical fiber communication systems

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