Figure 1
Symmetric solitons and vortices.
(a) The amplitude distribution in a stable symmetric fundamental soliton, for g = 1.1 and M = 20. (b) Dependence of the norm (M ≡ N) on the chemical potential (λ ≡ μ) for the family of fundamental symmetric solitons at different values of the cross-attraction coefficient, g. Solid lines depict stable numerically found solutions, while triangles represent the corresponding results produced by the VA as per Eqs (10)–(13). (c,d) Comparison of numerically found (solid lines) and VA-predicted (dashed lines) profiles of the fundamental symmetric solitons at g = 0.8, M = 40 (c) and g = 1.2, M = 40 (d). Panels (e) and (f) display, respectively the amplitude and phase distributions in a numerically found stable symmetric vortex solitons for g = 1.1 and M = 20. (g) Dependence of the norm (M ≡ N) on the chemical potential (λ ≡ μ) for the symmetric vortex solitons for different values of g. Solid and dashed lines represent stable and unstable vortices, respectively, while triangles depict the corresponding VA results, as per Eqs (16)–(19). At g > 1, the vortices are stable in a finite interval of values of the norm, see Eq. (6). (h) Dependence of the stability boundaries of vortices, Nmax and Nmin, on g. The gray regions in (b,g) represent the (narrow) first and second bands of the lattice-potential spectrum, respectively.
