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Resonant nonlinearity management for nonlinear-Schrödinger solitons

Hidetsugu Sakaguchi·Boris A. Malomed
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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 $ω$ 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 $ω$ 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 $ω$ 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.

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Hidetsugu Sakaguchi, Boris A. Malomed. 2004-10-27. Resonant nonlinearity management for nonlinear-Schrödinger solitons. https://doi.org/10.1103/physreve.70.066613

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