BÄCKLUND TRANSFORMATIONS FOR NON-COMMUTATIVE ANTI-SELF-DUAL YANG–MILLS EQUATIONS

GILSON, CLAIRE R. ; HAMANAKA, MASASHI ; NIMMO, JONATHAN J. C.

Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 83-93

Résumé

We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard.

Détail

DOI : 10.1017/S0017089508004801

Mots-clés : 35Q58, 46L55, 70S15

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