Reduction of Chern-Simons-Schrödinger Systems in One Space Dimension

Abstract

We study Chern-Simons-Schrödinger systems in one space dimension. We show that Chern-Simons-Schrödinger and $𝒩=\mathrm{2}$ supersymmetric Chern-Simons-Schrödinger equations can be reduced, under the gauge condition $A_{\mathrm{1}}\equiv \mathrm{0}$, to equations of $\varphi$, $\psi$ only which are coupled cubic Schrödinger systems.