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Bianchi Permutability for the Anti‐Self‐Dual Yang‐Mills Equations
Author(s) -
Benincasa Gregorio B.,
Halburd Rod
Publication year - 2016
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12118
Subject(s) - integrable system , mathematics , affine transformation , mathematical physics , dual (grammatical number) , transformation (genetics) , symmetry (geometry) , differential equation , matrix (chemical analysis) , pure mathematics , mathematical analysis , geometry , art , biochemistry , chemistry , materials science , literature , composite material , gene
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.