Bäcklund Transformations and Solution Hierarchies for the Third Painlevé Equation

Keywords

Mathematics, Discretization, Variety (cybernetics), Bessel function, Pure mathematics

References

• Rational solutions of the second and the fourth Painlevé equationsYoshihiro Murata — 1985
• The similarity solution for the Korteweg-de Vries equation and the related Painlevé transcendentRodolfo R. Rosales — 1978
• CYLINDRICAL WAVES IN GENERAL RELATIVITYJ. Rao — 1964
• Painlevé transcendents : their asymptotics and physical applicationsD. Levi, P. Winternitz — 1992
• Nonlinear Schrödinger equation, Bäcklund transformations and Painlevé transcendentsM. Boiti, F. Pempinelli — 1980
• A q-analog of the sixth Painlevé equationMichio Jimbo, Hidetaka Sakai — 1995
• Exact Linearization of a Painlevé TranscendentMark J. Ablowitz, Harvey Segur — 1977
• Method of isomonodromy deformations and asymptotics of the third Painlevé transcendentV. Yu. Novokshenov — 1984
• Über lineare homogene Differentialgleichungen zweiter Ordnung mit drei im Endlichen gelegenen wesentlich singulären StellenRichard Fuchs — 1907
• Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebraD. David, Niky Kamran, D. Levi — 1986
• Painlevé functions of the third kindBarry M. McCoy, Craig A. Tracy, Tai Tsun Wu — 1977
• Painlevé solution of the poisson-boltzmann equation for a cylindrical polyelectrolyte in excess salt solutionJohn S. McCaskill, Edward D. Fackerell — 1988
• On a Shallow Water Wave EquationP A Clarkson, E L Mansfield — 1994
• Painleve solutions in general relativityP. Wils — 1989
• Schlesinger transformations of Painlevé II‐VU. Muğan, A. S. Fokas — 1992
• On reduction of a two-dimensional generalized Toda lattice to an ordinary differential equations systemM. A. Gabeskiria, M. V. Saveliev — 1982
• Lax pairs, bäcklund transformations and special solutions for ordinary differential equationsJohn Gibbon, Alan C. Newell, M. Tabor — 1988
• New similarity reductions of the Boussinesq equationPeter A. Clarkson, Martin D. Kruskal — 1989
• From Continuous to Discrete Painlevé EquationsA. S. Fokas, B. Grammaticos, A. Ramani — 1993
• Painleve analysis of the non-linear Schrodinger family of equationsPeter A. Clarkson, C M Cosgrove — 1987

Cited by

• Consistent Composition of Bäcklund Transformations Produces Confined MapsClio Cresswell, Nalini Joshi — 2002
• The Painlevé III equation of type (0,0,4,-4), its associated vector bundles with isomonodromic connections, and the geometry of the movable polesMartin A. Guest, Claus Hertling — 2015
• New Transformations for Painlev\'e's Third TranscendentN. S. Witte — 2002
• Discrete equations and the singular manifold methodP.G. Estévez, Peter A. Clarkson — 1999
• Connection formulae for degenerated asymptotic solutions of the fourth Painleve equationAndrei Kapaev — 1998
• Sistemas Integrables: Propiedades y Estructuras SubyacentesJuan Manuel Conde Martín — 2012
• Solution Hierarchies for the Painlevé IV EquationDavid Bermúdez, David J. Fernández C. — 2011
• Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equationsPeter A. Clarkson — 2013
• First degree birational transformations of the Painleve equations and their contiguity relationsRobert Conte, Micheline Musette — 2001
• Painlevé equations: nonlinear special functionsPeter A. Clarkson — 2003
• Lower bounds and approximations of the locations of movable singularities of some nonlinear differential equations using parameterized bounded operatorsSteven G. From — 2006
• Rational solutions of the classical Boussinesq systemPeter A. Clarkson — 2009
• On Stieltjes relations, Painlevé-IV hierarchy and complex monodromyА. П. Веселов — 2000
• Solution of the equivalence problem for the third Painlevé equationYulia Yu. Bagderina, Николай Тарханов — 2015
• Mappings preserving locations of movable poles: II. The third and fifth Painlevé equationsPilar R. Gordoa, Nalini Joshi, Andrew Pickering — 2001
• The Symmetric Fourth Painlevé Hierarchy and Associated Special PolynomialsGalina Filipuk, Peter A. Clarkson — 2008
• New exact solutions of the discrete fourth Painleve´equationAndrew P. Bassom, Peter A. Clarkson — 1994
• On the Umemura polynomials for the Painlevé III equationKenji Kajiwara, Tetsu Masuda — 1999
• Special polynomials associated with rational solutions of the fifth Painlevé equationPeter A. Clarkson — 2005
• The second Painlevé equation, its hierarchy and associated special polynomialsPeter A. Clarkson, Elizabeth L. Mansfield — 2003

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