1202.1310 (V. Achilleos et al.)

Dark solitons and vortices in PT-symmetric nonlinear media: from
spontaneous symmetry breaking to nonlinear PT phase transitions    [PDF]

V. Achilleos, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González

We consider the nonlinear analogues of Parity-Time ($\mathcal{PT}$) symmetric
linear systems exhibiting defocusing nonlinearities. We study the ground state
and excited states (dark solitons and vortices) of the system and report the
following remarkable features. For relatively weak values of the parameter
$\varepsilon$ controlling the strength of the $\mathcal{PT}$-symmetric
potential, excited states undergo (analytically tractable) spontaneous symmetry
breaking; as $\varepsilon$ is further increased, the ground state and first
excited state, as well as branches of higher multi-soliton (multi-vortex)
states, collide in pairs and disappear in blue-sky bifurcations, in a way which
is strongly reminiscent of the linear $\mathcal{PT}$-phase transition ---thus
termed the nonlinear $\mathcal{PT}$-phase transition. Past this critical point,
initialization of, e.g., the former ground state leads to spontaneously
emerging "soliton (vortex) sprinklers".

View original: http://arxiv.org/abs/1202.1310