Noncommutative solitons and quasideterminants

作者：Hamanaka Masashi^*

来源：Physica Scripta, 2014, 89(3): 038006.

DOI：10.1088/0031-8949/89/03/038006

• anti-self-dual Yang-Mills equation
• Backlund transformation
• Penrose-Ward transformation
• Riemann-Hilbert problem
• quasideterminant

We discuss an extension of soliton theory and integrable systems to noncommutative spaces, focusing on integrable aspects of noncommutative anti-self-dual Yang-Mills equations. We give a wide class of exact solutions by solving a Riemann-Hilbert problem for the Atiyah-Ward ansatz and present Backlund transformations for the G = U(2) noncommutative anti-self-dual Yang-Mills equations. We find that noncommutative determinants of one kind, quasideterminants, play crucial roles in the construction of noncommutative solutions. We also discuss the reduction of a noncommutative anti-self-dual Yang-Mills equation to noncommutative integrable equations. This work is partially based on a collaboration with C R Gilson and J J C Nimmo (of Glasgow).

• 出版日期2014-3