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Zbl 1020.34011
Mansfield, Elizabeth L.; Webster, Helen N.
On one-parameter families of Painlevé III. (English)
[J] Stud. Appl. Math. 101, No.3, 321-341 (1998). ISSN 0022-2526; ISSN 1467-9590/e

Summary: Albrecht, Mansfield, and Milne developed a direct method with which one can calculate special integrals of polynomial type (also known as one-parameter family conditions, Darboux polynomials, eigenpolynomials, or algebraic invariant curves) for nonlinear ordinary differential equations of polynomial type. We apply this method to the third Painlevé equation and prove that, for the generic case, the set of known one-parameter family conditions is complete.

MSC 2000:: *34A55 Inverse problems of ODE
34A05 Methods of solution of ODE

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