Multi-Dimensional Weiss Operators - Borisenok, Sergey; Erkut, M. Hakan; Demirer, Murat; POLATOĞLU, YAŞAR (Scientific Technical Research Council Turkey-Tubitak, Ataturk Bulvari No 221, Kavaklidere, TR-06100 Ankara, Turkey, 2011)
We present a solution of the Weiss operator family generalized for the case of R(d) and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a subset of null class functions for a partial differential equation with the generalized Weiss operators. We illustrate the significance of our approach through several examples of both linear and non-linear partial differential equations.
Keywords: Partial Differential Equations; Weiss Operators; Painleve Property; Kısmi Diferansiyel Denklemler; Weiss Operatörler; Painleve Özelliği