Observation of a discrete family of transverse solitons in the presence of a symmetry-breaking bifurcation

Abstract

This report considers vectorial spatial solitons in a specific realization of a single-mirror feedback scheme displaying a symmetry-breaking pitchfork-bifurcation to two equivalent (or nearly equivalent) states. Numerical simulations of the microscopic model equations exhibit a family of discrete solitons and enable one to study the mechanism leading to the stabilization of the feedback solitons. It turns out that curvature-driven coarsening dynamics of a circular domain and 'pressure-induced' dynamics due to an imperfection of the symmetry-breaking bifurcation counteract. Solitary solutions can be obtained in a parameter region where an unstable equilibrium of these counteracting effects is stabilized by the vicinity of a small-amplitude modulational instability. An alternative method using a Newton algorithm to find stationary solutions of a radially symmetric system is used for studying the parameter dependencies of the bifurcation structure.