  We consider a three spin component Bose Einstein Condensate as described by
as many coupled nonlinear Schroedinger equations. For a very special ratio of
the coupling constants, exact N soliton solutions to this set of equations are
known. Here we find a simple representation including the N = 1 solution based
on the symmetry of the equations. This symmetry is described by a linear
operator, the nonlinearity of NLS notwithstanding. Our useful representation
opens the door to the nonintegrable case of general coupling constants. A new
class of solutions is found.

Quantum Gases