On One-Parameter Families of Painlevé III

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...

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Bibliographic Details
Published inStudies in applied mathematics (Cambridge) Vol. 101; no. 3; pp. 321 - 341
Main Authors Mansfield, Elizabeth L., Webster, Helen N.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Boston, USA and Oxford, UK Blackwell Publishers Inc 01.10.1998
Blackwell
Subjects
Exact sciences and technology
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
Special functions
Non linear equation
Eigenpolynomial
First order equation
Differential equation
Painlevé equation
Bäcklund transformation
Darboux problem
Integral
Algorithm
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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.
Bibliography:This article was presented at the Conference on Nonlinear Analysis, Solitons and PDEs, January 6-9, 1997, Sydney, Australia.
ArticleID:SAPM096
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istex:50F4D5B997BA91FEE762AF3FEDFA017375CD4FF1
ISSN:0022-2526
1467-9590
DOI:10.1111/1467-9590.00096