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Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6 Pt 2):066613. Epub 2004 Dec 13.

Resonant nonlinearity management for nonlinear Schrödinger solitons.

Author information

1
Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.

Abstract

We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to Bose-Einstein condensates in the context of the Feshbach-resonance control, and fiber-optic telecommunications as concerns periodic compensation of the nonlinearity. We find from simulations, and explain by means of a straightforward analysis, that the response of a fundamental soliton to the weak perturbation is resonant, if the modulation frequency omega is close to the intrinsic frequency of the soliton. For higher-order n-solitons with n=2 and 3, the response to an extremely weak perturbation is also resonant, if omega is close to the corresponding intrinsic frequency. More importantly, a slightly stronger drive splits the 2- or 3-soliton, respectively, into a set of two or three moving fundamental solitons. The dependence of the threshold perturbation amplitude, necessary for the splitting, on omega has a resonant character too. Amplitudes and velocities of the emerging fundamental solitons are accurately predicted, using exact and approximate conservation laws of the perturbed NLS equation.

PMID:
15697532
DOI:
10.1103/PhysRevE.70.066613

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