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Area of Science:

  • Nonlinear dynamics
  • Quantum mechanics
  • Optical physics

Background:

  • Vortex-ring structures are key solutions in nonlinear systems.
  • The interplay of Poisson and cubic nonlinearities influences vortex behavior.
  • Understanding stability and recurrence is crucial for nonlinear wave phenomena.

Purpose of the Study:

  • Investigate self-trapped vortex-ring eigenstates in 2D nonlinear Schrödinger equations.
  • Analyze the stability and long-term dynamics of these vortex solutions.
  • Explore the potential for recurrence phenomena and experimental realization.

Main Methods:

  • Solving the 2D Schrödinger equation with focusing Poisson and cubic nonlinearities.
  • Perturbative stability analysis of vortex-ring solutions.
  • Numerical simulations to track the evolution of unstable vortex states.

Main Results:

  • Identified families of vortex-ring solutions dependent on nonlinearity parameters.
  • Observed self-reconstruction and Fermi-Pasta-Ulam-Tsingou-type recurrence for topological charges l=1 and l=2.
  • Characterized stable and unstable regimes, identifying a strong stochasticity threshold.
  • Found all solutions for l≥3 to be unstable and nonrecurrent.

Conclusions:

  • Vortex-ring dynamics exhibit rich behavior, including recurrence, under combined nonlinearities.
  • The findings suggest a crossover to stochasticity in nonlinear wave systems.
  • Potential applications exist in nonlinear optics, particularly in thermo-optical media.