Painlevé test and linearization

The Painlevé test is a powerful tool to investigate the integrability of nonlinear ordinary and partial differential equations (see Steeb and Euler 1988 and references therein). In some cases the Painlevé test can lead to the linearization of the nonlinear differential equation. The nonlinear differential equation is considered in the complex domain. First we give a short introduction to ordinary differential equations and the Painlevé test. Then we describe the connection between the Painlevé property and the invertible point transformation. In chapter 8 we consider partial differential equations…