Characteristic Manifold and Painlevé Integrability: Fifth-Order Schwarzian Korteweg-de Type Equation

The single valued behaviour of the characteristic manifold is seldom considered when analysing the Painlevé property of a partial differential equation. Considering this, We take a simple example-the generalized fifth-order Schwarzian Korteweg-de Vries equation-to emphasize the usefulness to include the analysis of the single valued properties about the characteristic manifold in the Pianlevé test. The result shows that some types of Schwarzian equations may not be Painlevé integrable, though many of them may be.