Leznov, A. N.; Mukhtarov, M. A. Deformation of algebras and solution of self-duality equation. (English) Zbl 0663.35078 J. Math. Phys. 28, 2574-2578 (1987). The solutions of the self-duality equation depending on a set of functions of three independent variables are constructed in an explicit way. The obtained solutions are shown to be connected with two- dimensional systems determined by the operators of the Lax pair. Cited in 11 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 17B65 Infinite-dimensional Lie (super)algebras 35C05 Solutions to PDEs in closed form Keywords:deformation of algebras; infinite-dimensional solvable algebra; perturbative expansion series; Yang-Mills fields; self-duality equation; Lax pair PDFBibTeX XMLCite \textit{A. N. Leznov} and \textit{M. A. Mukhtarov}, J. Math. Phys. 28, 2574--2578 (1987; Zbl 0663.35078) Full Text: DOI References: [1] DOI: 10.1016/0167-2789(80)90010-X · doi:10.1016/0167-2789(80)90010-X [2] DOI: 10.1007/BF01029257 · Zbl 0547.35024 · doi:10.1007/BF01029257 [3] Kac V. G., Aiz. Akad. Nauk USSR, ser. Math. 32 pp 1323– (1968) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.