Darboux Transformations for a Lax Integrable System in 2n Dimensions
Darboux Transformations for a Lax Integrable System in 2n Dimensions
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DOI：
10.1007/s11005-997-3049-3
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发表时间：
1996-05
影响因子：
1.2
通讯作者：
Wenxiu Ma
中科院分区：
文献类型：
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作者：
Wenxiu Ma
通过一组特殊的谱问题，提出了一个2n维Lax可积系统.以高崎方程、自对偶Yang-Mills方程及其可积族为例。对这个Lax可积系统建立了达布变换的显式公式。Vandermonde和广义Cauchy行列式公式给出了导出显式解的描述，从而得到了一些有理解和解析解。
A 2n-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving explicit solutions and thus some rational and analytic solutions are obtained.