Ring-like two-breather structures of a partially nonlocal NLS system with different two-directional diffractions under a parabolic potential

Via a relation of the hypothetic solution, a variable-coefficient partially nonlocal nonlinear Schrodinger(NLS) system with different diffractions under a parabolic potential is associated with the constant-coefficient system. Ring-like two-breather solution of the variable-coefficient partially nonlocal NLS system is constructed by mapping the related solution of the constant-coefficient system. The characteristics of two-breather in the constant-coefficient system influence the properties of ring-like two-breather in the variable-coefficient partially nonlocal NLS system in xyz plane. In the xyz plane, the layer number of the ring-like two-breather along the z-direction augments with the add of the Hermite parameter.