论文标题
带有参数的PainlevéVI方程的Malgrange-Galois glopoid
Malgrange-Galois groupoid of Painlevé VI equation with parameters
论文作者
论文摘要
对于非常笼统的参数值，已知PainlevéIV方程的Malgrange-Galois Glopoid已知是相位空间的转换的伪群，该变换保留了体积形式，时间形式和方程。在这里，我们计算PainlevéVI家族的Malgrange-Galois群体，包括所有参数作为新的因变量。我们得出结论，它是保留参数值的转换的伪群，自变量的差异，因变量和方程中的体积形式。这意味着，根据参数的分析，PainlevéVI的解决方案不能满足任何新的偏微分方程（包括衍生物W。r。t。参数），该方程并非源自PainlevéVI。
The Malgrange-Galois groupoid of Painlevé IV equations is known to be, for very general values of parameters, the pseudogroup of transformations of the phase space preserving a volume form, a time form and the equation. Here we compute the Malgrange-Galois groupoid of Painlevé VI family including all parameters as new dependent variables. We conclude it is the pseoudogroup of transformations preserving parameter values, the differential of the independent variable, a volume form in the dependent variables and the equation. This implies that a solution of Painlevé VI depending analytically on parameters does not satisfy any new partial differential equation (including derivatives w. r. t. parameters) which is not derived from Painlevé VI.
