an:01591522
Zbl 0961.37024
Filchakova, Valentina P.
PP-test for integrability of some evolution differential equations
EN
Proceedings of the third international conference on symmetry in nonlinear mathematical physics, Kyiv, Ukraine, July 12-18, 1999. Part 2. Transl. from the Ukrainian. Kyiv: Institute of Mathematics of NAS of Ukraine. Proc. Inst. Math. Natl. Acad. Sci. Ukr., Math. Appl. 30(2), 387-391 (2000).
2000
a
37K10 34M55 37K20
nonlinear partial differential equation; Painlev?? transcendent; singularity analysis; inverse scattering method; singular manifold method
The author discusses the problem of connection between Painlev?? 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 Painlev?? property, i.e., all its removable singularities are poles. The author gives a survey of corresponding results and suggests a procedure for constructing the Painlev?? 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)].
For the entire collection see [Zbl 0937.00046].
I.O.Parasyuk (Ky??v)
Zbl 0333.65001