To describe dynamical systems we usually make suitable approximations in the hope of finding valid descriptions of their characteristic quantities. But even after such approximations we mostly cannot write down explicitly how these quantities depend on time, usually such a dependence is much to complicated to be computed explicitly. Therefore we commonly write down dynamical systems in their in...

The Painlevé test is a widely applied and quite successful technique to investigate the integrability [8] of nonlinear ODEs and PDEs by analyzing the singularity structure of the solutions. The test is named after the French mathematician Paul Painlevé (1863-1933) [18], who classified second order differential equations that are solvable in terms of known elementary functions or new transcenden...