Modulation analysis of large-scale discrete vortices

Area of Science:

• Nonlinear dynamics
• Condensed matter physics
• Mathematical physics

Background:

• The discrete nonlinear Schrödinger equation models various physical phenomena, including light propagation in photonic lattices and Bose-Einstein condensates.
• Vortices, or localized wave structures, are crucial in these systems, but their stability and behavior in discrete lattices are complex.
• Previous studies primarily focused on the anticontinuum limit, leaving behavior away from this limit less explored.

Purpose of the Study:

• To investigate the behavior and stabilization mechanisms of large-scale vortices in discrete nonlinear systems.
• To analyze circular, polygonal, and straight vortices beyond the anticontinuum limit.
• To identify conditions leading to the formation of long-lived, localized structures.

Main Methods:

• Application of a discrete version of modulation theory to analyze vortex dynamics.
• Numerical simulations of large-scale circular, polygonal, and straight vortices.
• Investigation of vortex stabilization by self-consistent potentials and standing waves.

Main Results:

• Vortices are trapped and stabilized by the Peierls-Nabarro potential they generate within the lattice.
• Large-scale circular and polygonal vortices exhibit stable behavior away from the anticontinuum limit.
• Straight structures are stabilized by nonconstant mean levels created by standing waves at their ends.
• Numerical evidence for the existence of long-lived, localized, quasiperiodic structures.

Conclusions:

• Self-consistent Peierls-Nabarro potentials play a key role in vortex stabilization in discrete nonlinear systems.
• The study extends the understanding of vortex behavior in discrete systems beyond the anticontinuum limit.
• The findings suggest the possibility of creating and maintaining complex localized structures in discrete nonlinear media.