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Interface solitons in locally linked two-dimensional lattices.

M D Petrović¹, G Gligorić, A Maluckov

¹Vinca Institute of Nuclear Sciences, University of Belgrade, P.O.B. 522, 11001 Belgrade, Serbia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 21, 2011

Summary

We investigated soliton complexes in coupled 2D lattices, finding that antisymmetric solitons exist broadly. Symmetric and asymmetric solitons appear below a critical coupling, with symmetry breaking leading to stable asymmetric modes.

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Area of Science:

Nonlinear physics
Optical lattice dynamics
Soliton theory

Background:

Soliton complexes are crucial in nonlinear systems.
Understanding their stability in coupled lattices is essential for applications.

Purpose of the Study:

Investigate the existence, stability, and dynamics of soliton complexes.
Analyze these complexes centered at a single transverse link between two 2D lattices.

Main Methods:

Modeling using discrete nonlinear Schrödinger equations with onsite cubic self-focusing nonlinearity.
Employing variational approximation (VA) and numerical simulations.
Analyzing symmetric, antisymmetric, and asymmetric soliton complexes.

Main Results:

Antisymmetric soliton complexes exist across the entire parameter space.
Symmetric and asymmetric modes exist below a critical coupling parameter.
Symmetry breaking leads to stable asymmetric modes; antisymmetric modes show instabilities in specific regions.

Conclusions:

The study predicts and confirms the behavior of different soliton complex types.
Bistability allows coexistence of stable antisymmetric solitons with symmetric or asymmetric ones.
Findings offer insights into nonlinear dynamics in coupled lattice systems.