论文标题
SU的解决方案（$ \ MATHCAL {N} $）自助Yang-Mills方程
Solutions to the SU($\mathcal{N}$) self-dual Yang-Mills equation
论文作者
论文摘要
在本文中，我们旨在通过任意$ \ Mathcal {n} $来得出SU（$ \ MATHCAL {N} $）的SU（$ \ MATHCAL {N} $）方程的解决方案。引入了一组非交通关系来构建一个可以简化为SDYM方程的矩阵方程。结果表明，这些关系可以从两个不同的sylvester方程生成，这对应于（矩阵）的两个cauchy矩阵方案，分别是Kadomtsev-PetviaShvili层次结构和（矩阵）Ablowitz-Kaup-Newell-Newell-segur-segur-segur-segur层次。在每种Cauchy矩阵方案中，我们研究可能导致SU $（\ Mathcal {n}）$ SDYM方程的可能减少，还分析了某些解决方案的物理意义，即是隐性化，阳性，确定性的，并且确定性是一个。
In this paper we aim to derive solutions for the SU($\mathcal{N}$) self-dual Yang-Mills (SDYM) equation with arbitrary $\mathcal{N}$. A set of noncommutative relations are introduced to construct a matrix equation that can be reduced to the SDYM equation. It is shown that these relations can be generated from two different Sylvester equations, which correspond to the two Cauchy matrix schemes for the (matrix) Kadomtsev-Petviashvili hierarchy and the (matrix) Ablowitz-Kaup-Newell-Segur hierarchy, respectively. In each Cauchy matrix scheme we investigate the possible reductions that can lead to the SU$(\mathcal{N})$ SDYM equation and also analyze the physical significance of some solutions, i.e. being Hermitian, positive-definite and of determinant being one.
