  A finite-size quasi two-dimensional Bose-Einstein condensate collapses if the
attraction between atoms is sufficiently strong. Here we present a theory of
collapse for condensates with the interatomic attraction and spin-orbit
coupling. We consider two realizations of spin-orbit coupling: the axial Rashba
coupling and balanced, effectively one-dimensional, Rashba-Dresselhaus one. In
both cases spin-dependent "anomalous" velocity, proportional to the spin-orbit
coupling strength, plays a crucial role. For the Rashba coupling, this velocity
forms a centrifugal component in the density flux opposite to that arising due
to the attraction between particles and prevents the collapse at a sufficiently
strong coupling. For the balanced Rashba-Dresselhaus coupling, the
spin-dependent velocity can spatially split the initial state in one dimension
and form spin-projected wavepackets, reducing the total condensate density.
Depending on the spin-orbit coupling strength, interatomic attraction, and the
initial state, this splitting either prevents the collapse or modifies the
collapse process. These results show that the collapse can be controlled by a
spin-orbit coupling, thus, extending the domain of existence of condensates of
attracting atoms.
