Noncommutative Integrable Systems and Quasideterminants
arXiv:1012.6043 · doi:10.1063/1.3367025
Abstract
We discuss extension of soliton theories and integrable systems into noncommutative spaces. In the framework of noncommutative integrable hierarchy, we give infinite conserved quantities and exact soliton solutions for many noncommutative integrable equations, which are represented in terms of Strachan's products and quasi-determinants, respectively. We also present a relation to an noncommutative anti-self-dual Yang-Mills equation, and make comments on how "integrability" should be considered in noncommutative spaces.
16 pages. Based on invited talks at the World Conference on Nonlinear Analysts (WCNA), Orlando, 2-9 July 2008 and the International Workshop on Nonlinear and Modern Mathematical Physics (NMMP), Beijing, 15-21 July 2009
References in corpus (8)
- Komaba Lectures on Noncommutative Solitons and D-Branes
- On Noncommutative Solitons
- Exact Noncommutative KP and KdV Multi-solitons
- Noncommutative Solitons and D-branes
- Noncommutative Supersymmetric/Integrable Models and String Theory
- Extension of Moyal-deformed hierarchies of soliton equations
- Noncommutative Solitons and Integrable Systems
- Topics in noncommutative integrable theories and holographic brane-world cosmology