TY - JOUR

T1 - Symmetry breaking in linearly coupled dynamical lattices

AU - Herring, G.

AU - Kevrekidis, P. G.

AU - Malomed, B. A.

AU - Carretero-González, R.

AU - Frantzeskakis, D. J.

PY - 2007/12/27

Y1 - 2007/12/27

N2 - We examine one- and two-dimensional models of linearly coupled lattices of the discrete-nonlinear-Schrödinger type. Analyzing ground states of the system with equal powers (norms) in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the total power. 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 two-dimensional lattice solitons. This feature has no counterpart in the continuum limit because of the collapse instability in the latter case.

AB - We examine one- and two-dimensional models of linearly coupled lattices of the discrete-nonlinear-Schrödinger type. Analyzing ground states of the system with equal powers (norms) in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the total power. 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 two-dimensional lattice solitons. This feature has no counterpart in the continuum limit because of the collapse instability in the latter case.

UR - http://www.scopus.com/inward/record.url?scp=37649024908&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.76.066606

DO - 10.1103/PhysRevE.76.066606

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AN - SCOPUS:37649024908

SN - 1539-3755

VL - 76

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 6

M1 - 066606

ER -