The Lax Pair by Dimensional Reduction of Chern-Simons Gauge Theory

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.

27 pages, Plain Tex

References in corpus (3)

• Classical Symmetries of Some Two-Dimensional Models
• Lineal gravity from planar gravity
• One Formulation for both Lineal Gravities through a Dimensional Reduction

Cited by in corpus (3)

• Integrable dissipative structures in the gauge theory of gravity
• Gravity assisted solution of the mass gap problem for pure Yang-Mills fields
• Moving Frames Hierarchy and BF Theory