By: Boris A. Malomed
From: Tel Aviv University, Israel
At: Instituto de Investigação Interdisciplinar, Anfiteatro
Many important configurations in optical and matter-wave (Bose-Einstein condensate) systems are based on settings with two parallel cores (waveguides), coupled by tunneling of photons or atoms. Basic models of such media amount to systems of linearly coupled equations with nonlinearities acting in each equation. A well-known example is the model of dual-core optical fibers or planar waveguides, which amounts to a system of linearly coupled nonlinear Schroedinger (NLS) equations. Similar models apply to BEC loaded into a set of parallel one- or two-dimensional tunnel-coupled traps. In such models, obvious symmetric soliton solutions lose their stability through symmetry-breaking bifurcations, when the total energy (norm) exceeds a certain critical value (i.e., the nonlinearity acting in the cores becomes strong enough). The bifurcations, which are typically of the sub- and supercritical types in the cases of the self-attractive and repulsive signs of the intrinsic nonlinearity, respectively, give rise to asymmetric solitons. These two types of the symmetry-breaking bifurcations are similar, severally, to the general phase transitions of the first and second kinds. The talk aims to present an overview of basic models, results, and physical realizations of the symmetry-breaking phenomena in conservative and dissipative dual-core nonlinear media, including continual and discrete systems.