...beyond-mean-field effects Lee–Huang–Yang corrections vortex droplets semidiscrete modes Theoretical Models of QDs in Three, Two, and One Dimensions The 3D case The energy density of a condensed Bose–Bose mixture in the MF (mean-field) approximation is (11.1) E MF = 1 2 g 11...

..., the lattice structure of the so designed multi-core waveguide was made hexagonal. It is shown, along with the family of the corresponding transverse Bloch modes, in Fig. 8.12 . This setup makes it possible to stabilize both 2D spatial solitons and 3D spatiotemporal modes (LBs). FIG. 8.12 The left panel...

... ) with coefficients different from the specific value N ( N + 1 ) , generate a mixture of solitons and quasi-linear waves, alias “radiation modes,” which spread in the course of the evolution. In terms of the IST for KdV and other integrable equations, solitons are represented by the discrete...