Coupled density-spin Bose-Einstein condensates dynamics and collapse in systems with quintic nonlinearity

We investigate the effects of spin-orbit coupling and Zeeman splitting on the coupled density-spin dynamics and collapse of the Bose-Einstein condensate driven by the quintic self-attraction in the same- and cross-spin channels. The characteristic feature of the collapse is the decrease in the width as given by the participation ratio of the density rather than by the expectation values of the coordinate. Qualitative arguments and numerical simulations reveal the existence of a critical spin-orbit coupling strength which either prohibits or leads to the collapse, and its dependence on other parameters, such as the condensates norm, spin-dependent nonlinear coupling, and the Zeeman splitting. The entire nonlinear dynamics critically depend on the initial spin sate.