中文摘要：

从带负幂次谱参数的谱问题出发,构造了一类广义自对偶Yang-Mills方程.这类方程包括若干著名的Lax可积方程,如Takasaki情形、Belavin-Zakharov情形、AblowitzChakravarty-Takhtajall情形和Ma情形.进而建立了这类方程的达布变换的精确表达式.

英文摘要：

A generalized self-dual Yang-Mills equation with negative powers of the spectral parameter is proposed by a set of spectral problems. It contains some well-known Lax integrable equations such the Takasaki case, the Belavin-Zakharov case, the Ablowitz-Chakravarty- Takhtajan case and the Ma case. The explicit formulation of Darboux transformation is established for this equation.