Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 083, 9 pages      arXiv:0708.3506      http://dx.doi.org/10.3842/SIGMA.2007.083
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Stability Analysis of Continuous Waves in Nonlocal Random Nonlinear Media

Maxim A. Molchan
B.I. Stepanov Institute of Physics, 68 Nezalezhnasci Ave., 220072 Minsk, Belarus

Received July 26, 2007, in final form August 15, 2007; Published online August 26, 2007

Abstract
On the basis of the competing cubic-quintic nonlinearity model, stability (instability) of continuous waves in nonlocal random non-Kerr nonlinear media is studied analytically and numerically. Fluctuating media parameters are modeled by the Gaussian white noise. It is shown that for different response functions of a medium nonlocality suppresses, as a rule, both the growth rate peak and bandwidth of instability caused by random parameters. At the same time, for a special form of the response functions there can be an ''anomalous'' subjection of nonlocality to the instability development which leads to further increase of the growth rate. Along with the second-order moments of the modulational amplitude, higher-order moments are taken into account.

Key words: nonlocality; competing nonlinearity; stochasticity.

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