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Sayed, S. M.; Gharib, G. M.

Canonical reduction of self-dual Yang-Mills equations to Fitzhugh-Nagumo equation and exact solutions. (English) Zbl 1197.35139

Chaos Solitons Fractals 39, No. 2, 492-498 (2009).
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.

Cited in 5 Documents

MSC:

35K55 Nonlinear parabolic equations

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ATFM
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\textit{S. M. Sayed} and \textit{G. M. Gharib}, Chaos Solitons Fractals 39, No. 2, 492--498 (2009; Zbl 1197.35139)
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References:

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