A SELF-DUAL BOGOMOLNYI FORMULATION OF THE NONLINEAR SCHRODINGER-EQUATION

We obtain a self-dual formulation of the conventional nonlinear Schrod inger equation (NLSE) in the 1+1 dimension by studying the dimensional reduction of the self-dual Chern-Simons nonlinear Schrodinger model ( NLSM) in the 2+1 dimension. It is found that this self-dual formulatio n allows us to find not only the well-known soliton solutions from the Bogomol'nyi bound and the Galilean boost, but also other soliton solu tions in the presence of the background sources. (C) 1997 Elsevier Sci ence B.V.