One- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with fractional kinetic energy

We address effects of spin-orbit coupling (SOC), phenomenologically added to a two-component Bose-Einstein condensate composed of particles moving by Lévy flights, in one- and two-dimensional (1D) and (2D) settings. The corresponding system of coupled Gross-Pitaevskii equations includes fractional kinetic-energy operators, characterized by the Lévy index, α < 2 (the normal kinetic energy corresponds to α = 2). The SOC terms, with strength λ, produce strong effects in the 2D case: they create families of stable solitons of the semi-vortex and mixed-mode types in the interval of 1 < α < 2, where the supercritical collapse does not admit the existence of stable solitons in the absence of the SOC. At λ → 0, amplitudes of these solitons vanish 1/4λ 1/(α-1).