  We propose a method to analytically solve the one-dimensional coupled
nonlinear Gross-Pitaevskii equations which govern the motion of the spinor
Bose-Einstein condensates. In a uniform external potential, the Hamiltonian
comprises the kinetic energy, the linear and the quadratic Zeeman energies.
Several classes of exact periodic and solitonic solutions, either in real or in
complex forms, are obtained for both the F=1 and F=2 condensates. These
solutions are general that contain neither approximations nor constraints on
the system parameters.
