We consider nonlinear analogues of Parity-Time (PT) symmetric linear systemsexhibiting defocusing nonlinearities. We study the ground state and excitedstates (dark solitons and vortices) of the system and report the followingremarkable features. For relatively weak values of the parameter $\varepsilon$controlling the strength of the PT-symmetric potential, excited states undergo(analytically tractable) spontaneous symmetry breaking; as $\varepsilon$ isfurther increased, the ground state and first excited state, as well asbranches of higher multi-soliton (multi-vortex) states, collide in pairs anddisappear in blue-sky bifurcations, in a way which is strongly reminiscent ofthe linear PT-phase transition ---thus termed the nonlinear PT-phasetransition. Past this critical point, initialization of, e.g., the formerground state leads to spontaneously emerging solitons and vortices.
展开▼
