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Two-dimensional discrete solitons in rotating lattices.

Jesús Cuevas1, Boris A Malomed, P G Kevrekidis

  • 1Departamento de Física Aplicada I, Escuela Universitaria Politécnica, C/ Virgen de Africa, 7, 41011 Sevilla, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
PubMed
Summary

We studied the two-dimensional discrete nonlinear Schrödinger equation in a rotating frame, finding that rotation can stabilize vortex solitons (VSs) with S=2, while destabilizing those with S=1. This impacts Bose-Einstein condensates and nonlinear fiber optics.

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Area of Science:

  • Nonlinear Optics
  • Quantum Physics
  • Condensed Matter Physics

Background:

  • The discrete nonlinear Schrödinger (DNLS) equation models phenomena like Bose-Einstein condensates and nonlinear light propagation.
  • Understanding the stability of localized states (solitons) in these systems is crucial for their practical applications.
  • Rotation introduces Coriolis forces, potentially altering the dynamics and stability of solitons.

Purpose of the Study:

  • To investigate the impact of rotation on localized states in the two-dimensional DNLS equation with self-attractive cubic nonlinearity.
  • To construct and analyze the stability of off-axis fundamental solitons (FSs) and on-axis vortex solitons (VSs) with different vorticities (S=1, S=2).
  • To determine the conditions under which rotation stabilizes or destabilizes these soliton solutions.

Main Methods:

  • Analytical construction of off-axis fundamental solitons and on-axis vortex solitons (S=1, S=2).
  • Numerical analysis of soliton stability by examining eigenvalues of the linearized system.
  • Systematic variation of rotation frequency (Ω) and lattice coupling constant (C) to map stability regions.

Main Results:

  • Fundamental solitons (FSs) exhibit a stability interval dependent on rotation frequency and lattice coupling.
  • Vortex solitons (VSs) with S=1 are destabilized by rotation in the weak-coupling limit.
  • Vortex solitons (VSs) with S=2, typically unstable, are stabilized by rotation within specific parameter regimes.

Conclusions:

  • Rotation plays a critical role in the stability of localized states in the 2D DNLS equation.
  • Specific soliton types can be stabilized or destabilized by rotation, offering potential control mechanisms.
  • The findings have implications for controlling Bose-Einstein condensates and light propagation in rotating nonlinear systems.