Symmetry Breaking in Linearly Coupled Dynamical Lattices

Details Symmetry Breaking in Linearly Coupled Dynamical Lattices Symmetry Breaking in Linearly Coupled Dynamical Lattices

2007-04-25

arxiv.org/abs/0704.3284v1

Phys. Rev. E 76 (2007) 066606

Nonlinear Sciences

Pattern Formation and Solitons

9 pages, 9 figures, submitted to Phys. Rev. E, Apr, 2007

Scientific paper

10.1103/PhysRevE.76.066606

We examine one- and two-dimensional (1D and 2D) models of linearly coupled lattices of the discrete-nonlinear-Schr{\"{o}}dinger type. Analyzing ground states of the systems with equal powers in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the squared $l^2$-norm. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking in 2D lattice solitons. This feature has no counterpart in the continuum limit, because of the collapse instability in the latter case.

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