[soliton-dual-core]{}. The same type of the transition may be featured by CW (continuous-wave) states in dual-core systems with non-Kerr nonlinearities [@Snyder].

In addition to the analysis of static symmetric and asymmetric modes, dynamical regimes, most typically in the form of oscillations of the mean-field wave function between two wells of the DWP structure, were analyzed too. Following the analogy with Josephson oscillations of the wave function of Cooper-paired electrons in superconducting tunnel junctions [Ustinov]{}, the possibility of oscillations in *bosonic Josephson junctions* was predicted [@junction]. The simplest dynamical model of the Josephson oscillations in bosonic systems was derived by means of the tight-binding approximation ([@superconductor]).

Experimental manifestations of the SSB have been observed in both BEC and photonics. Self-trapping of a macroscopically asymmetric state of the atomic condensate of $^{87}$Rb atoms, loaded into the DWP, as well as Josephson oscillations in that setting, were reported in Ref. [@Markus] (in that case, the effective nonlinearity is self-repulsive, therefore the respective SSB occurs not in the symmetric GS, but rather in the antisymmetric first excited state). The SSB of laser beams coupled into an effective transverse DWP created in the self-focusing photorefractive medium was demonstrated in Ref. [@photo]. Other experimentally observed SSB 