The nonlinear focusing or collapse is considered for the superposed magnetic fluids in motion at uniform speeds. The magnetic field is applied along the direction of streaming. It is shown that the evolution of the amplitude is governed by a two‐dimensional Schro¨dinger equation with cubic nonlinearity. This equation gives rise to a self‐focusing singularity when the velocity difference is in the subcritical regime. It is shown that such a self‐focusing effect is direction dependent, and predominant at shorter wavelengths.