Backlund transformations of MKdV and Painleve equations

Keywords

Scaling, Transformation (genetics), Space (punctuation), Linear map, Algebra over a field

References

• Rational solutions of the second and the fourth Painlevé equationsYoshihiro Murata — 1985
• Painlevé transcendents : their asymptotics and physical applicationsD. Levi, P. Winternitz — 1992
• Nonlinear Schrödinger equation, Bäcklund transformations and Painlevé transcendentsM. Boiti, F. Pempinelli — 1980
• Studies on the Painlevé equations II. Fifth Painlevé equation PVKazuo Okamoto — 1987
• The Nonlinear Schrodinger Equation and Conserved Quantities in the Deformed Parafermion and SL(2,R)/U(1) Coset ModelsJeremy Schiff — 1992
• Unitary matrix models and 2D quantum gravityS. Dalley, Clifford V. Johnson, Tim R. Morris — 1992
• Elements of Soliton Theory (G. L. Lamb, Jr.)John W. Miles — 1983
• On a unified approach to transformations and elementary solutions of Painlevé equationsA. S. Fokas, Mark J. Ablowitz — 1982
• Self-duality and the Painleve transcendentsLionel Mason, N M J Woodhouse — 1993
• Similarity solutions of the Korteweg-de Vries equationM. Boiti, F. Pempinelli — 1979
• The Painlevé property for partial differential equationsJohn Weiss, M. Tabor, G. F. Carnevale — 1983
• Solitons, Nonlinear Evolution Equations and Inverse ScatteringM. A. Ablowitz, Peter A. Clarkson — 1992
• On the antiplectic pair connected with the Adler-Gel'fand-Dikii bracketGeorge Wilson — 1992
• Linearization of the Boussinesq equation and the modified Boussinesq equationG. Quispel, Frank Nijhoff, H.W. Capel — 1982
• Lie algebras and equations of Korteweg-de Vries typeVladimir Drinfeld, В. В. Соколов — 1985
• Studies on the Painleve equations IIK. Okamoto — 1987
• Studies on the Painlev equations: III. Second and fourth painlev equations,P II andP IVKazuo Okamoto — 1986
• Solitons, Nonlinear Evolution Equations and Inverse Scattering: ReferencesM. Ablowitz, Peter A. Clarkson — 1991

Cited by

• 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
• The fourth Painlevé equation and associated special polynomialsPeter A. Clarkson — 2003
• Special Polynomials Associated with Rational Solutions of the Painlevé Equations and Applications to Soliton EquationsPeter A. Clarkson — 2006
• Truncation-type methods and Bäcklund transformations for ordinary differential equations: the third and fifth Painlevé equationsPilar R. Gordoa, Nalini Joshi, Andrew Pickering — 2000
• The third Painlevé equation and associated special polynomialsPeter A. Clarkson — 2003
• A dynamical systems approach to the fourth Painlevé equationJeremy Schiff, Michael Twiton — 2018
• From KP/UC hierarchies to Painleve equationsTeruhisa Tsuda — 2010
• Gauge symmetry origin of Bäcklund transformations for Painlevé equationsV C C Alves, H Aratyn, J F Gomes — 2021
• On Hamiltonian Formalism for Dressing Chain Equations of Even PeriodicityH. Aratyn, J. F. Gomes, A. H. Zímerman — 2021
• Higher Time-Derivative Theories from Space–Time Interchanged Integrable Field TheoriesAndreas Fring, Takano Taira, Bethan Turner — 2024
• Extended Symmetry of Higher Painlevé Equations of Even Periodicity and Their Rational SolutionsH. Aratyn, J. F. Gomes, G. V. Lobo — 2024
• Integrability Analysis of the Generalized (2+1)-dimensional Hirota-Satsuma-Ito Equation Based on Bell Polynomial MethodJiangying Huo, Taogetusang Bao — 2024
• Painlevé Equations and Associated PolynomialsPeter A. Clarkson — 2005
• A Vector Bilinear Framework for Soliton Dynamics in Coupled Modified KdV SystemsLaurent Delisle, Amine Jaouadi — 2026

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