Vector solitons of a one-dimensional spatially inhomogeneous coupled nonlinear Schrödinger equation with a double well potential

Vector soliton solutions of a coupled nonlinear Schrödinger equation with spatially inhomogeneous nonlinearities and a double well potential are studied. A type of non-auto-Bäcklund transformations is established to cast the investigated system to a couple of constant coefficient NLS equations under general conditions associating the inhomogeneous nonlinearities with the external potential. It is seen that the judicious choice of the inhomogeneous nonlinear interactions and the external potential is critical in the transformation work. In detail, three types of vector solitons are explicitly presented, and their structures and stability properties are also discussed.