Bessel vortices in spin-orbit-coupled binary Bose–Einstein condensates with Zeeman splitting

We present an analysis of stationary solutions for two-dimensional (2D) Bose-Einstein condensates (BECs) with the Rashba spin-orbit (SO) coupling and Zeeman splitting. By introducing generalized momentum operator, linear version system can be solved exactly. The are semi-vortices Bessel-vortex (BV) modified (MBV) types, in presence weak strong splitting, respectively. ground states (GSs) full nonlinear constructed help a specially designed neural network (NN). GS mixed-mode type appears as cross-attraction interaction increases. spin texture is produced detail. It exhibits Neel skyrmion structure semi-vortex BV type, respective number found analytical form. On other hand, GSs MBV types do not form skyrmions.