  We find analytic continuous wave (cw) solutions for spinor Bose-Einstein
condenates (BECs) in a magnetic field that are more general than those
published to date. For particles with spin F=1 in a homogeneous one-dimensional
trap, there exist cw states in which the chemical potential and wavevectors of
the different spin components are different from each other. We include linear
and quadratic Zeeman splitting. Linear Zeeman splitting, if the magnetic field
is constant and uniform, can be mathematically eliminated by a gauge
transformation, but quadratic Zeeman effects modify the cw solutions in a way
similar to non-zero differences in the wavenumbers between the different spin
states. The solutions are stable fixed points within the continuous wave
framework, and the coherent spin mixing frequencies are obtained.
