On Soliton Content of Self Dual Yang-Mills Equations

Details On Soliton Content of Self Dual Yang-Mills Equations On Soliton Content of Self Dual Yang-Mills Equations

1993-11-19

arxiv.org/abs/hep-th/9311119v1

Phys.Lett. A183 (1993) 293-300

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, plain Tex

Scientific paper

10.1016/0375-9601(93)90459-D

Exploiting the formulation of the Self Dual Yang-Mills equations as a Riemann-Hilbert factorization problem, we present a theory of pulling back soliton hierarchies to the Self Dual Yang-Mills equations. We show that for each map $ \C^4 \to \C^{\infty } $ satisfying a simple system of linear equations formulated below one can pull back the (generalized) Drinfeld-Sokolov hierarchies to the Self Dual Yang-Mills equations. This indicates that there is a class of solutions to the Self Dual Yang-Mills equations which can be constructed using the soliton techniques like the $\tau$ function method. In particular this class contains the solutions obtained via the symmetry reductions of the Self Dual Yang-Mills equations. It also contains genuine 4 dimensional solutions . The method can be used to study the symmetry reductions and as an example of that we get an equation exibiting breaking solitons, formulated by O. Bogoyavlenskii, as one of the $2 + 1 $ dimensional reductions of the Self Dual Yang-Mills equations.

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