IJPAM: Volume 94, No. 3 (2014)

EXACT SOLUTIONS AND CANONICAL REDUCTION OF
THE SELF-DUAL YANG MILLS EQUATIONS TO
SOME NONLINEAR EVOLUTION EQUATIONS

A.R. Shehata$^1$, J.F.Alzaidy$^2$
$^1$Mathematics Department
Faculty of Science
Minia University, El-Minia, EGYPT
$^2$Mathematics Department
Faculty of Science
Taif University
KINGDOM OF SAUDI ARABIA


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 solutions for the original two dimensional Burgers equation, Hunter-Saxton equation and Nonlinear diffusion. 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 Bäcklund transformations with the aid of Mathematica , either the seed solution is constant or a traveling wave.

Received: January 2, 2014

AMS Subject Classification: 35, 53C, 58J, 58Z05

Key Words and Phrases: SDYM, Burgers equation, Hunter-Saxton equation, nonlinear diffusion equation, Bäcklund transformations

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DOI: 10.12732/ijpam.v94i3.5 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 94
Issue: 3
Pages: 355 - 372

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).