Noncommutative Integrable Systems and Quasideterminants
Mathematical Physics
2015-05-20 v1 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1012.6043,
title = {Noncommutative Integrable Systems and Quasideterminants},
author = {Masashi Hamanaka},
journal= {arXiv preprint arXiv:1012.6043},
year = {2015}
}
Comments
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