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 solutions for the original two dimensional complex Ginzburg-Landau equation. The corresponding gauge potential A(mu) and the gauge field strengths F-mu nu 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 using the Backlund transformations with the aid of Mathematica, either the seed solution is constant or a traveling wave.