Continuous-wave solutions in spinor Bose-Einstein condensates

We find analytic continuous-wave (cw) solutions for spinor Bose-Einstein condensates in a magnetic field that are more general than other published solutions. For particles with spin F=1 in a homogeneous one-dimensional trap, there exist cw states in which the chemical potential and wave vectors 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 nonzero differences in the wave numbers between the different spin states. The solutions are stable fixed points within the continuous-wave framework, and the coherent spin mixing frequencies are obtained.