Diverging probability density functions for flat-top solitary waves - Nonlinear Sciences > Pattern Formation and Solitons

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Abstract: We investigate the statistics of flat-top solitary wave parameters in thepresence of weak multiplicative dissipative disorder. We consider firstpropagation of solitary waves of the cubic-quintic nonlinear Schr\-odingerequation CQNLSE in the presence of disorder in the cubic nonlinear gain. Weshow by a perturbative analytic calculation and by Monte Carlo simulations thatthe probability density function PDF of the amplitude $\eta$ exhibitsloglognormal divergence near the maximum possible amplitude $\eta {m}$, abehavior that is similar to the one observed earlier for disorder in the lineargain A. Peleg et al., Phys. Rev. E {\bf 72}, 027203 2005. We relate theloglognormal divergence of the amplitude PDF to the super-exponential approachof $\eta$ to $\eta {m}$ in the corresponding deterministic model withlinear-nonlinear gain. Furthermore, for solitary waves of the derivative CQNLSEwith weak disorder in the linear gain both the amplitude and the group velocity$\beta$ become random. We therefore study analytically and by Monte Carlosimulations the PDF of the parameter $p$, where$p=\eta-1-\varepsilon s\beta-2$ and $\varepsilon s$ is the self-steepeningcoefficient. Our analytic calculations and numerical simulations show that thePDF of $p$ is loglognormally divergent near the maximum $p$-value.

Autor: Avner Peleg, Yeojin Chung, Tomáš Dohnal, Quan M. Nguyen

Fuente: https://arxiv.org/