Self-consistent turbulence in the two-dimensional nonlinear Schrödinger equation with a repulsive potential

Area of Science:

• Nonlinear physics
• Fluid dynamics
• Quantum mechanics

Background:

• The study investigates dark solitons, which are localized intensity decreases in wave functions.
• Dark solitons in two-dimensional nonlinear Schrödinger (NLS) equation dynamics exhibit unique behaviors due to energy and angular momentum radiation.
• Previous research on incompressible media provides a contrast to the radiation dynamics observed here.

Purpose of the Study:

• To analyze the breakup of multicharged dark solitons into single-charge vortices.
• To characterize the resulting turbulent motion and vortex distribution.
• To identify the fundamental rules governing the steady turbulent state.

Main Methods:

• Analytical investigation of dark soliton dynamics.
• Numerical simulations of vortex breakup and evolution.
• Application of Lyapunov functional extremization to determine steady states.

Main Results:

• Multicharged dark solitons fragment into chaotically moving single-charge vortices after initial wave radiation.
• A steady, spatially confined turbulent motion of vortices emerges, forming distinct orbits.
• Vortex distribution is independent of container size beyond the initial soliton's potential well.
• Steady states are governed by the absence of Cherenkov resonance and potential energy maximization.

Conclusions:

• The turbulent vortex motion exhibits self-organization into stable orbits.
• The dynamics are primarily dictated by sound velocity and energy principles, not container size.
• The findings offer insights into self-organized criticality in nonlinear systems.