Summary
We write down without proof a class of integrable nonlinear partial differential equations containing as one of its members the 4-dimensional Yang-Mills equation together with its associated Darboux and Bäcklund transformations.
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References
M. Bruschi, D. Levi andO. Ragnisco:The chiral field hierarchy, preprint I.F.U. No. 271 (1981), submitted for pubblication toPhys. Lett. A.
V. E. Zakharov andA. V. Mikhailov:Sov. Phys. JETP,47, 1017 (1978).
See for instance,Ling-Lie Chau Wang:Bianchi-Bäcklund transformations, conservation laws and linearization of various field theories. A status report, talk delivered at theInternational Workshop on High-Energy Physics held at Serpukhov, September 22–28, 1980, and references therein quoted.
See, for instance:D. Levi andR. Benguria:Proc. Nat. Acad. Sci. USA,77, 5025 (1980);M. Bruschi andO. Ragnisco:Lett. Nuovo Cimento,29, 327 (1980);D. Levi andO. Ragnisco:Bäcklund transformations for chiral field equations, preprint I. F. U. No. 268, submitted for pubblication toPhys. Lett. A.
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The research reported in this letter has been partially supported by CNR grant No. 80.02459.02 and Nato grant No. 057.81.
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Bruschi, M., Levi, D. & Ragnisco, O. Nonlinear partial differential equations and bäcklund transformations related to the 4-dimensional self-dual Yang-Mills equations. Lett. Nuovo Cimento 33, 263–266 (1982). https://doi.org/10.1007/BF02725447
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DOI: https://doi.org/10.1007/BF02725447