The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory
Oktay K. Pashaev
Abstract
We show that the Nonlinear Schrödinger Equation and the related Lax pair in 1+1 dimensions can be derived from 2+1 dimensional Chern-Simons Topological Gauge Theory. The spectral parameter, a main object for the Loop algebra structure and the Inverse Spectral Transform, has appear as a homogeneous part (condensate) of the statistical gauge field, connected with the compactified extra space coordinate. In terms of solitons, a natural interpretation for the one-dimensional analog of Chern-Simons Gauss law is given.
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