Bianchi permutability for the anti-self-dual Yang-Mills equations

2016/01/12 by Gregorio Benincasa, Benincasa, Gregorio, Rod Halburd +1
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.1601.03102

15 pages. To appear in Studies in Applied Mathematics

arxiv created 2016/01/12 · arxiv updated 2016/01/14

Abstract

The anti-self-dual Yang-Mills equations are known to have reductions to many integrable differential equations. A general Bäcklund transformation (BT) for the 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.

Related

• Self-Dual Yang-Mills and the Hamiltonian Structures of Integrable Systems
• Backlund Transformations for Darboux Integrable Differential Systems
• On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations
• Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces
• Discrete and Backlund (!) transformations of SDYM system