An extended representation of three-spin-component Bose–Einstein condensate solitons

We consider a three-spin-component Bose–Einstein condensate as described by as many coupled nonlinear Schrödinger 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 means of a linear operator, the nonlinearity of the NLS equations notwithstanding. Our useful representation opens the door to considering the nonintegrable case of general coupling constants. A new class of solutions is found.