of the SSB and self-trapping phase transitions should take place in generic DWP structures.

These arguments can be cast in a more definite form, if the central barrier in Eq. (\[potential\]) is approximated by $H_{\mathrm{central}}(x)=A\delta
(x)$, and the outer barriers are made impenetrable, similar to what is shown in Fig. \[symmetric and asymmetric modes\](c). These conjectures replace the present model by the one for an infinitely deep potential box split by delta-functional barrier, which is the simplest model of the SSB [NaturePhot2,Chili]{}. In the limit of large $A$, the latter model predicts the following value of the norm at the SSB bifurcation point,$$N_{\mathrm{bif}}\approx 8\pi ^{2}/\left( 3l^{2}A\right)   \label{analyt}$$(see caption to Fig. 2 in Ref. [@NaturePhot2]), where $l/2$ is the coordinate of the point at which the wave function vanishes (half-width of the infinitely deep box). In particular, one can identify $l\simeq 9$ for $%
A=0.5$ in Fig. \[symmetric and asymmetric modes\](b), hence Eq. ([analyt]{}) yields $N_{\mathrm{bif}}~\simeq 0.65$, while the respective numerical  value in Fig. \[bifurcation point\](b) is $N_{\mathrm{bif}%
}~\approx 0.62$, which implies a reasonable agreement for the present (not really large) value of $A$.

Evolution of unstable symmetric states
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Conclusions concerning the stability and instability of the symmetric and asymmetric 