The cosgrove’s sd-i equation and b¨acklund transformations of painlev´e equations

الملخص EN

In this article, we studied the usage of the one-to-one correspondence between a given Painlev´e equation and a certain second-order second-degree Painlev´e-type equation to derive the Backland transformations for the given Painlev´e equation.

We showed that all basic Backland transformations of the second, third, and fourth Painlev´e equations can be derived by using the one-to-one correspondences between these equations and the Cosgrove’s SD-I equation