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Resonant nonlinearity management for nonlinear Schrödinger solitons
Hidetsugu Sakaguchi1, Boris A Malomed
1Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 9, 2005
Summary
Periodic modulation of nonlinearity affects solitons in the nonlinear Schrödinger equation (NLS). Fundamental and higher-order solitons exhibit resonant responses to perturbations near their intrinsic frequencies, with potential for splitting.
Area of Science:
- Nonlinear dynamics
- Quantum physics
- Optical communications
Background:
- The nonlinear Schrödinger equation (NLS) models phenomena in Bose-Einstein condensates and fiber optics.
- Periodic modulation of nonlinearity is relevant for Feshbach-resonance control and nonlinearity compensation.
Purpose of the Study:
- Investigate the impact of periodic nonlinearity modulation on solitons.
- Analyze the resonant behavior and splitting of solitons under perturbation.
Main Methods:
- Numerical simulations of the perturbed NLS equation.
- Analytical explanations using conservation laws.
- Analysis of soliton response to periodic perturbations.
Main Results:
- Fundamental solitons show resonant response to weak perturbations at specific modulation frequencies.
- Higher-order solitons (n=2, 3) also exhibit resonant behavior.
- Stronger perturbations can split higher-order solitons into multiple fundamental solitons.
Conclusions:
- Soliton behavior is highly sensitive to the frequency of nonlinearity modulation.
- The splitting of higher-order solitons is a key finding with potential applications.
- Conservation laws accurately predict the properties of emergent solitons.