Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2004-10-27
Nonlinear Sciences
Pattern Formation and Solitons
14 pages, 6 figures
Scientific paper
10.1103/PhysRevE.70.066613
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.
Malomed Boris A.
Sakaguchi Hidetsugu
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