Abstract
The (constrained) canonical reduction of four-dimensional self- dual Yang-Mills (SDYM) theory to two-dimensional Burgers equation, Hunter- Saxton equation and Nonlinear diffusion equation are considered. On the other hand, other methods and transformations are developed to obtain exact solu- tions for the original two dimensional Burgers equation, Hunter-Saxton equa- tion and Nonlinear diffusion. The corresponding gauge potential Aµ and the gauge field strengths Fµν 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.
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