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Zbl 1197.35139
Sayed, S.M.; Gharib, G.M.
Canonical reduction of self-dual Yang-Mills equations to Fitzhugh-Nagumo equation and exact solutions. (English)
[J] Chaos Solitons Fractals 39, No. 2, 492-498 (2009). ISSN 0960-0779

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. \par 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 2000:: *35K55 Nonlinear parabolic equations

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Zentralblatt MATH Berlin [Germany]