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Light bullets in coupled nonlinear Schrödinger equations with variable coefficients and a trapping potential.
Optics Express
|April 26, 2017
Summary
Researchers explored stable three-dimensional (3D) vector solitary waves, or light bullets, in nonlinear systems. Only low-order vortex soliton pairs demonstrated stability within a composite trap, while higher-order ones proved unstable.
Area of Science:
- Nonlinear Optics
- Mathematical Physics
- Soliton Theory
Background:
- Coupled nonlinear Schrödinger equations model wave propagation in various media.
- Three-dimensional (3D) vector solitary waves, known as light bullets (LBs), are localized wave packets.
- Spatially modulated potentials introduce complex dynamics to wave systems.
Purpose of the Study:
- To investigate the existence and stability of 3D vector solitary waves in a system with spatially modulated diffraction, nonlinearity, and a trapping potential.
- To identify the conditions under which vortex 3D LB pairs can be stably propagated.
- To determine the limitations of higher-order LBs in such modulated systems.
Main Methods:
- Utilized the self-similarity method to find exact solutions for vector solitary waves.
- Employed direct numerical simulations to analyze the stability of vortex 3D LB pairs.
- Investigated the influence of a composite self-consistent trapping potential on wave dynamics.
Main Results:
- Exact solutions for 3D vector solitary waves (light bullets) were derived.
- Stability analysis revealed that only low-order vortex soliton pairs (n ≤ 1, l ≤ 1, m = 0) are stable.
- Higher-order 3D LBs were found to be unstable over extended propagation distances.
Conclusions:
- The study identifies specific conditions for stable propagation of 3D vector solitary waves in modulated nonlinear systems.
- Low-order vortex soliton pairs represent robust solutions within the composite trapping potential.
- Higher-order light bullets are susceptible to instabilities in these complex environments.
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