Application to the Noumi-Yamada System with a Large Parameter

Abstract

It is known that a traditional Painlevé equation (of the variable t) is obtained by the compatibility condition of a system of second order linear differential equations of the variables x and t. Here, when we focus upon the underlying linear system, the latter variable t is often called a deformation parameter. We can consider, with the appropriate introduction of a large parameter $\eta$ into these systems, the Stokes geometry for both the linear and non-linear systems in the same way as that described in the previous chapter.