Some reductions of the self‐dual Yang–Mills equations to integrable systems in 2+1 dimensions
Some reductions of the self‐dual Yang–Mills equations to integrable systems in 2+1 dimensions
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DOI：
10.1063/1.531155
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发表时间：
1995-02
影响因子：
1.3
通讯作者：
S. Chakravarty;S. L. Kent;E. Newman
中科院分区：
文献类型：
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作者：
S. Chakravarty;S. L. Kent;E. Newman
研究了自对偶杨-米尔斯（SDYM）方程的约化，通过施加两个时空对称性，并要求连接单形式属于一个辅助变量中的形式矩阵值微分算子的李代数。本文研究了2×2矩阵的纯量情形和典型情形。在标量情况下，它表明，场方程可以减少到强迫Burgers方程。在矩阵情形下，得到了几个著名的2+1可积方程。还审查了某些2+1方程的解决方案之间的转换性质。
A reduction of the self‐dual Yang–Mills (SDYM) equations is studied by imposing two space–time symmetries and by requiring that the connection one‐form belongs to a Lie algebra of formal matrix‐valued differential operators in an auxiliary variable. In this article, the scalar case and the canonical cases for 2×2 matrices are examined. In the scalar case, it is shown that the field equations can be reduced to the forced Burgers equation. In the matrix case, several well‐known 2+1 integrable equations are obtained. Also examined are certain transformation properties between the solutions of some of these 2+1 equations.