Noncommutative solitons and quasideterminants
Noncommutative solitons and quasideterminants
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DOI：
10.1088/0031-8949/89/03/038006
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发表时间：
2010-12
期刊：
影响因子：
2.9
通讯作者：
M. Hamanaka
中科院分区：
文献类型：
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作者：
M. Hamanaka
我们讨论了孤子理论和可积系统在非对易空间的推广，重点讨论了非对易反自对偶的Yang-Mills方程的可积性。我们通过求解Atiyah-Ward ansatz的Riemann-Hilbert问题给出了一类广泛的精确解，并给出了G=U(2)非对易反自对偶Yang-Mills方程的Bäck lund变换。我们发现一类非对易行列式，即拟行列式，在非对易解的构造中起着至关重要的作用。我们还讨论了非对易反自对偶的Yang-Mills方程化为非对易可积方程的问题。这项工作部分是基于与C·R·吉尔森和J·J·C·尼莫(格拉斯哥的)的合作。
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 Bäcklund 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).