Geodesic
BÄCKLUND TRANSFORMATIONS FOR NON-COMMUTATIVE ANTI-SELF-DUAL YANG–MILLS EQUATIONS
Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 83-93

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DOI

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.
DOI : 10.1017/S0017089508004801
Mots-clés : 35Q58, 46L55, 70S15 
GILSON, CLAIRE R.; HAMANAKA, MASASHI; NIMMO, JONATHAN J. C. BÄCKLUND TRANSFORMATIONS FOR NON-COMMUTATIVE ANTI-SELF-DUAL YANG–MILLS EQUATIONS. Glasgow mathematical journal, Tome 51 (2009) no. A, pp. 83-93. doi: 10.1017/S0017089508004801
@article{10_1017_S0017089508004801,
     author = {GILSON, CLAIRE R. and HAMANAKA, MASASHI and NIMMO, JONATHAN J. C.},
     title = {B\"ACKLUND {TRANSFORMATIONS} {FOR} {NON-COMMUTATIVE} {ANTI-SELF-DUAL} {YANG{\textendash}MILLS} {EQUATIONS}},
     journal = {Glasgow mathematical journal},
     pages = {83--93},
     year = {2009},
     volume = {51},
     number = {A},
     doi = {10.1017/S0017089508004801},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004801/}
}
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