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Solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity
P G Kevrekidis1, B A Malomed, Yu B Gaididei
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
We investigated localized states in nonlinear Schrödinger equations on 2D lattices. Lattice type and interaction range significantly impact soliton stability, with vortices often decaying into fundamental solitons.
Area of Science:
- Nonlinear physics
- Condensed matter theory
- Mathematical physics
Background:
- Localized states are crucial in nonlinear systems.
- Discrete nonlinear Schrödinger equation (DNLS) models wave phenomena.
- Nonsquare lattices introduce complex geometries.
Purpose of the Study:
- To investigate the existence and stability of localized states in 2D DNLS on nonsquare lattices.
- To analyze the influence of nearest-neighbor and long-range interactions.
- To explore complex localized modes like vortices.
Main Methods:
- Numerical simulations of the discrete nonlinear Schrödinger equation.
- Analysis of lattice coordination numbers.
- Direct simulations of vortex dynamics.
Main Results:
- Soliton stability depends on lattice coordination number and interaction range.
- Long-range interactions can destabilize or stabilize solitons based on their sign relative to short-range interactions.
- Vortices on triangular and honeycomb lattices often decay into fundamental solitons.
Conclusions:
- Lattice geometry and interaction types critically determine localized state stability in 2D DNLS.
- Complex localized modes exhibit unique stability properties and decay mechanisms.
- The study provides insights into wave localization in complex discrete systems.