Canonical reduction of self-dual Yang-Mills theory to Burgers, sine-Gordon, generalized KdV, Liouville's equations and exact solutions
Faculty of Sciences. Physics
RELATIVITY ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS
Il Nuovo cimento della societÓ italiana di fisica : B: General physics, relativity, astronomy and mathematical physics and methods. - -, 1985 - 2008
, p. 147-163
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.