Backlund transformations and the Atiyah-Ward ansatz for non-commutative anti-self-dual Yang-Mills equations

被引：12

作者：

Gilson, Claire R. ^{[2
]}

Hamanaka, Masashi ^{[1
]}

Nimmo, Jonathan J. C. ^{[2
]}

机构：

[1] Nagoya Univ, Dept Math, Nagoya, Aichi 4648602, Japan

[2] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2009年 / 465卷 / 2108期

关键词：

non-commutative integrable systems; anti-self-dual Yang-Mills equation; quasi-determinant solutions; Atiyah-Ward ansatz; Penrose-Ward transformation; QUASIDETERMINANT SOLUTIONS; DARBOUX TRANSFORMATIONS; INTEGRABLE SYSTEMS; KP HIERARCHY; FIELD-THEORY; INSTANTONS; DETERMINANTS; CONSTRUCTION;

D O I：

10.1098/rspa.2008.0515

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We present Backlund transformations for the non-commutative anti-self-dual Yang Mills equation 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. We also explain the origins of all the ingredients of the Backlund transformations within the framework of non-commutative twistor theory. In particular, we show that the generated solutions belong to a non-commutative version of the Atiyah-Ward ansatz.

引用

页码：2613 / 2632

页数：20

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