The symmetry algebra of the planar nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge fields is systematically determined. It is confirmed to be the semidirect sum of the eight dimensional Schrodinger algebra sch(2) (with no central extension) and of the infinitesimal gauge transformation algebra. The conditional symmetries that arise when self-duality is imposed are also discussed and found to have, as expected, a Kac-Moody-Virasoro structure. Several examples of symmetry reductions to ordinary differential equations are presented and non-self-dual solutions are obtained. The non-self-dual system is shown not to have the Painleve property. (C) 1994 Acadmic Press, Inc.
LEVI D, VINET L, & WINTERNITZ P (1994). SYMMETRIES AND CONDITIONAL SYMMETRIES OF A NONRELATIVISTIC CHERN-SIMONS SYSTEM. ANNALS OF PHYSICS, 230(1), 101-117 [10.1006/aphy.1994.1018].