Symmetry breaking in linearly coupled dynamical lattices

Authors

G Herring
PG Kevrekidis, University of Massachusetts - AmherstFollow
BA Malomed
R Carretero-Gonzalez
DJ Frantzeskakis

Publication Date

2007

Journal or Book Title

PHYSICAL REVIEW E

Abstract

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.

Comments

This is the pre-published version harvested from arXiv. The published version is located at http://pre.aps.org/abstract/PRE/v76/i6/e066606

Pages

-

Volume

76

Issue

6

Recommended Citation

Herring, G; Kevrekidis, PG; Malomed, BA; Carretero-Gonzalez, R; and Frantzeskakis, DJ, "Symmetry breaking in linearly coupled dynamical lattices" (2007). PHYSICAL REVIEW E. 104.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/104