Abstract
Inspired by Sato's new theory for soliton equations, we find a new approach to the self-dual Yang-Mills equations. We first establish a correspondence of solutions between the self-dual Yang-Mills equations and a new system of equations with infinitely many unknown functions. It then turns out that the latter equations can be easily solved by a simple explicit procedure. This leads to an explicit description of a very broad class of solutions to the self-dual Yang-Mills equations, and also to a construction of transformations acting on these solutions.
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Takasaki, K. A new approach to the self-dual Yang-Mills equations. Commun.Math. Phys. 94, 35–59 (1984). https://doi.org/10.1007/BF01212348
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DOI: https://doi.org/10.1007/BF01212348