### Equivalence and nonexistence of standing waves for coupled Schrodinger equations with Chern-Simons gauge fields

DOI: http://dx.doi.org/10.12775/TMNA.2015.056

#### Abstract

This paper is devoted to the study of standing waves for so-called $N=2$ supersymmetric Chern--Simons--Schrodinger equations, a coupled system of Schr\"odinger 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.

#### Keywords

N=2 supersymmetric Chern-Simons-Schrodinger; critical coupling constants; self-dual system

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