*(English)*Zbl 1197.35139

Summary: The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional Fitzhugh-Nagumo and the real Newell-Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh-Nagumo and Newell-Whitehead equations. The corresponding gauge potential $A\mu $ and the gauge field strengths $F\mu \nu $ are also obtained. New explicit and exact traveling wave and solitary solutions (for Fitzhugh-Nagumo and Newell-Whitehead equations) are obtained by using an improved sine-cosine method and the Wu’s elimination method with the aid of Mathematica.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:

35K55 | Nonlinear parabolic equations |