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 NN-soliton solutions to this set of equations are known. Here we find a simple representation including the N=1N=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.

► We show that all bright solitons in an F=1F=1 spinor BEC are special cases of oscillatons.
► We show that the equations describing a single oscillaton reduce to a Manakov system.
► We stress the importance of rotational symmetry in spin space in a nonlinear system.