Stationary solutions and dynamical evolution of the nonlocal Gross–Pitaevskii equation in spin-2 Bose–Einstein condensates

Abstract

In this paper, we investigate the nonlocal Gross–Pitaevskii equation which describes the phenomena of Bose–Einstein condensates under the mean field approximation. Using mean-field theory and adopting separation of variables method, the five-component Gross–Pitaevskii spin–orbit-coupled spin-2 Bose–Einstein condensate model can be reduced to five-component ordinary differential equation, then twelve families of solutions are obtained by the combination of some Jacobi elliptic functions. In particular, when the modulus of Jacobi elliptic function tends to one, a series of bright soliton and dark soliton and their combined solution are obtained. These periodic and hyperbolic soliton solutions are analyzed in detail, the nature and images will be of practical application to provide theoretical guidance for spin systems.