PP-test for integrability of some evolution differential equations (Q2711763)

The author discusses the problem of connection between Painlevé transcendent and integrability of nonlinear PDE. This discussion is based on the Ablowitz-Ramani-Segur conjecture that every ODE obtained by similarity reduction from a PDE solvable with the inverse scattering method possesses the Painlevé property, i.e., all its removable singularities are poles. The author gives a survey of corresponding results and suggests a procedure for constructing the Painlevé transcendents. This procedure includes an algorithm of isolation of poles proposed by the author and uses the method of generalized power series developed by \textit{P. F. Filtschakow} [Numerische und graphische Methoden der angewandten Mathematik. Braunschweig: Friedr. Vieweg (1975; Zbl 0333.65001)].NEWLINENEWLINEFor the entire collection see [Zbl 0937.00046].