Canonical Reduction of the Self-Dual Yang Mills Equations to Complex Ginzburg-Landau Equations and Exact Solutions

Abstract

The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills
(SDYM) theory to two-dimensional complex Ginzburg-Landau equation are considered.  On the other hand, other methods and transformations are developed to obtain exact solu-tions for the original two dimensional complex Ginzburg-Landau equation. The corres-ponding gauge potential  and the gauge field strengths are also obtained. For these nonlinear evolution equations (NLEEs) which describe pseudo-spherical surfaces (pss) two new exact solution classes are generated from known solutions by us-ing the B̈cklund transformations with the aid of Mathematica,either the seed solution is constant or a traveling wave.