Soliton-Limited Superflow in 3He-A Between Parallel Plates

We have studied theoretically the flow of superfluid 3He-A in parallel-plate geometry. The equilibrium order-parameter texture is calculated numerically in two spatial dimensions consisting of the coordinates along the flow direction and perpendicular to the plates. The calculations have been done using the hydrostatic theory in the Ginzburg-Landau region and assuming a large external magnetic field perpendicular to the plane of calculation. We have studied a uniform texture and a dipole-unlocked splay soliton as initial configurations. In the former case we find the Freedericksz transition and a helical instability with increasing flow. In the latter case we find instability in the soliton. This instability is closely related to the critical velocity in the presence of a vortex sheet. Also, the transverse NMR frequency shift at the soliton has been calculated.