([potential]{})\], in Fig. \[bifurcation point\]. In panel (\[bifurcation\_k\]), the boundary between the SSB occurring with the delocalized and trapped modes ($k_{\mathrm{bif}}<0$ and $k_{\mathrm{bif}}>0$, respectively) is located at $A\approx 0.30$, the same value corresponding to the boundary designated by the square symbol in panel \[bifurcation\_N\]). That is, the SSB happens first (at smaller $N$) at $A>0.30$, while the transition to the self-trapping precedes the SSB at $A<0.30$.

The fact that the SSB happens with the trapped and leaky modes, respectively, at small and large $A$, as seen in Fig. \[bifurcation point\], is easy to explain: small $A$ implies strong linear coupling between the wave functions in the two barely separated wells, hence very large $N$ is required to induce the SSB, being far greater than the value of $N$ needed for the onset of the self-trapping, which is determined by the fixed parameters of the outer barrier in the DWP structure (\[potential\]). On the contrary, large $A$ implies weak linear coupling between the strongly separated wells, hence the respective strength of the nonlinearity (measured by $N$), required for the SSB, is much smaller than the value necessary for the commencement of the self-trapping. These arguments clearly suggest that the same sequence 