Bäcklund Transformations for Noncommutative Anti-Self-Dual Yang-Mills Equations
arXiv:0709.2069 · doi:10.1017/S0017089508004801
Abstract
We present Backlund transformations for the noncommutative 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 quasideterminants and belong to a noncommutative version of the Atiyah-Ward ansatz. In commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard.
10 pages; version to appear in Glasgow Mathematical Journal
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Cited by in corpus (6)
- Noncommutative Solitons and Quasideterminants
- The ADHM Construction of Instantons on Noncommutative Spaces
- Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
- Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
- Soliton Scattering in Noncommutative Spaces
- A new bidirectional generalization of (2+1)-dimensional matrix k-constrained KP hierarchy