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Published on: December 4, 2017
Chaoticons described by nonlocal nonlinear Schrödinger equation.
Lanhua Zhong1,2, Yuqi Li3, Yong Chen3
1Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou 510631, P.R. China.
Unstable Hermite-Gauss solutions to a nonlocal nonlinear Schrödinger equation can become chaotic states, termed chaoticons. These entities display both chaotic and soliton-like properties, including invariant width and quasi-elastic collisions.
Area of Science:
- Nonlinear dynamics
- Mathematical physics
- Optical solitons
Background:
- Nonlinear Schrödinger equation (NLSE) models wave propagation in various media.
- Stationary solutions like Hermite-Gauss modes are fundamental.
- Nonlocal NLSEs incorporate long-range interactions, leading to complex dynamics.
Purpose of the Study:
- Investigate the stability of Hermite-Gauss-type stationary solutions.
- Explore the transition from stable to chaotic dynamics in a nonlocal NLSE.
- Characterize novel emergent phenomena in nonlinear wave systems.
Main Methods:
- Numerical simulations of the nonlocal nonlinear Schrödinger equation.
- Analysis of Lyapunov exponents to quantify chaos.
- Examination of statistical width and collision properties.
Main Results:
- Unstable Hermite-Gauss solutions evolve into chaotic states.
- These states, termed 'chaoticons', exhibit positive Lyapunov exponents and spatial decoherence.
- Chaoticons maintain a stable statistic width and undergo quasi-elastic collisions.
Conclusions:
- Chaoticons represent a new class of complex wave entities.
- They bridge the gap between chaotic behavior and soliton characteristics.
- This finding expands the understanding of nonlinear wave phenomena and chaos theory.
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