Canonical reduction of self-dual Yang-Mills theory to Burgers, sine-Gordon, generalized KdV, Liouville's equations and exact solutions
Canonical reduction of self-dual Yang-Mills theory to Burgers, sine-Gordon, generalized KdV, Liouville's equations and exact solutions
Faculty of Sciences. Physics

article

2005
2005

Physics

RELATIVITY ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS

Il Nuovo cimento della società italiana di fisica : B: General physics, relativity, astronomy and mathematical physics and methods. - -, 1985 - 2008

120(2005)
:2
, p. 147-163

1594-9982

000231781000003

E

English (eng)

University of Antwerp

The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to Burgers' type, two-dimensional sine-Gordon, generalized Korteweg-de Vries-type, (2+1.)- and the original (3+1)-dimensional Liouville equations are considered. On the one hand, the Backlund transformations are implemented to obtain several classes of exact solutions for the reduced Burgers-type and two-dimensional sine-Gordon equations. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional generalized Korteweg-de Vries-type, (2+1)- and the original (3+1)-dimensional Lionville equations. The corresponding gauge potential A(mu v) and the gauge field strengths F-mu v are also obtained.

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