EQUIVALENCE AND NONEXISTENCE OF STANDING WAVES FOR COUPLED SCHRODINGER EQUATIONS WITH CHERN-SIMONS GAUGE FIELDS

This paper is devoted to the study of standing waves for so-called N = 2 supersymmetric Chern-Simons-Schrodinger equations, a coupled system of Schrodinger equations in which Chern-Simons gauge fields are incorporated. We show that there is no nontrivial standing wave to the N = 2 supersymmetric Chern-Simons-Schrodinger equations when the coupling constants are less than critical numbers. We also prove that static N = 2 supersymmetric Chern-Simons-Schrodinger equations are equivalent to their first order self-dual system when the coupling constants are critical.