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Updated: Oct 1, 2025
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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
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Nonlinear Schrödinger waves in a disordered potential: Branched flow, spectrum diffusion, and rogue waves.
1Institute of Fluid Mechanics, Beihang University, Beijing 100191, China.
Chaos (Woodbury, N.Y.)
|March 2, 2022
Summary
Nonlinear Schrödinger waves in disordered potentials exhibit complex behaviors. Increased nonlinearity leads to branched soliton flows and rogue waves, with spectral broadening suppressed by potential correlation length.
Area of Science:
- Physics
- Nonlinear Dynamics
- Wave Phenomena
Background:
- Nonlinear Schrödinger (NLS) waves in disordered potentials are crucial in hydrodynamics, optics, and cold atoms.
- Studying the interplay between nonlinearity and random effects in NLS waves is an ongoing challenge with incomplete results.
Purpose of the Study:
- To systematically simulate turbulent waves for the focusing NLS equation with dynamical random potentials.
- To investigate the evolution of branching structures and the occurrence of rogue waves.
- To analyze the spectral properties and the influence of nonlinearity and potential correlation length.
Main Methods:
- Systematic numerical simulations of the focusing NLS equation.
- Analysis of dynamical (time-dependent) random potentials.
- Nonlinear spectral analysis to understand soliton dynamics and wave evolution.
Main Results:
- Enhanced branching structures evolve into branched soliton flows with increasing nonlinearity.
- Rogue waves occur at short times due to linear random focusing and modulation instability.
- At longer times, rogue waves result from self-organization of larger solitons and breakup of intermediate ones.
- Strong nonlinearity broadens the linear spectrum but suppresses its spreading rate, dependent on potential correlation length.
Conclusions:
- The study provides insights into the complex dynamics of NLS waves in disordered media.
- Findings clarify the mechanisms behind rogue wave formation and spectral evolution.
- The results enhance understanding of the interaction between nonlinearity and random effects in wave systems.
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