Truncation-type methods and Bäcklund transformations for ordinary differential equations: the third and fifth Painlevé equations

Keywords

Mathematics, Truncation (statistics), Ordinary differential equation, Type (biology), Differential equation

References

• Backlund transformations of MKdV and Painleve equationsJ Schiff — 1993
• Studies on the Painlevé equations II. Fifth Painlevé equation PVKazuo Okamoto — 1987
• On a unified approach to transformations and elementary solutions of Painlevé equationsA. S. Fokas, Mark J. Ablowitz — 1982
• Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equationsPilar R. Gordoa, Nalini Joshi, Andrew Pickering — 1999
• Bäcklund Transformations and Solution Hierarchies for the Third Painlevé EquationAlice E. Milne, Peter A. Clarkson, Andrew P. Bassom — 1995
• THE PAINLEVE PROPERTY FOR PARTIAL DIFFERENTIAL EQUATIONS. II. BACKLUND TRANSFORMATION, LAX PAIRS, AND THE SCHWARZIAN DERIVATIVEJohn Weiss — 1983
• Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approachPeter A. Clarkson, Nalini Joshi, Andrew Pickering — 1998
• Studies on the Painleve equations IIK. Okamoto — 1987
• Bäcklund Transformations of Painlevé Equations and Their ApplicationsV. Gromak — 1999
• Backlund Transformations of MKdV and Painlevé EquationsJeremy Schiff — 1993

Cited by

• New Transformations for Painlev\'e's Third TranscendentN. S. Witte — 2002
• Asymptotic behaviour of the fifth Painlevé transcendents in the space of initial valuesNalini Joshi, Milena Radnović — 2017
• Mappings preserving locations of movable poles: II. The third and fifth Painlevé equationsPilar R. Gordoa, Nalini Joshi, Andrew Pickering — 2001
• Backlund transformations for higher order Painleve equationsPilar R. Gordoa, U. Muğan, Andrew Pickering — 2004
• Backlund transformations for fourth-order Painleve-type equationsA. H. Sakka, Safejan R. Elshamy — 2005
• Auto‐Bäcklund Transformations for New Matrix First and Second Painlevé HierarchiesPilar R. Gordoa, Andrew Pickering — 2024
• Painlevé Tests, Singularity Structure and IntegrabilityAndrew N. W. Hone — 2005

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