Bianchi Permutability for the Anti-Self-Dual Yang-Mills Equations

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• 作者：Gregorio B. Benincasa and Rod Halburd
• 刊名：Studies in Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：137
• 期：1
• 页码：110-122
• 全文大小：115K
• ISSN：1467-9590

文摘

The anti-self-dual Yang-Mills equations are known to have reductions to many integrable differential equations. A general Bäcklund transformation (BT) for the anti-self-dual Yang-Mills (ASDYM) equations generated by a Darboux matrix with an affine dependence on the spectral parameter is obtained, together with its Bianchi permutability equation. We give examples in which we obtain BTs of symmetry reductions of the ASDYM equations by reducing this ASDYM BT. Some discrete integrable systems are obtained directly from reductions of the ASDYM Bianchi system.