Nonlinear Modes and Symmetries in Linearly Coupled Pairs of math formula-Invariant Dimers

Authors


Abstract

The subjects of the work are pairs of linearly coupled math formula-symmetric dimers. Two different settings are introduced, namely, straight-coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross-coupled dimers, with each gain site coupled to two lossy ones. The latter pair with equal coupling coefficients represents a math formula-hypersymmetric quadrimer. We find symmetric and antisymmetric solutions in these systems, chiefly in an analytical form, and explore the existence, stability, and dynamical behavior of such solutions by means of numerical methods. We thus identify bifurcations occurring in the systems, including spontaneous symmetry breaking and saddle-center bifurcations. Simulations demonstrate that evolution of unstable branches typically leads to blowup. However, in some cases, unstable modes rearrange into stable ones.

Ancillary