Higher-order nonlinear special functions: Painlevé hierarchies, a survey
From MaRDI portal
Publication:6649508
DOI10.1090/conm/807/16169MaRDI QIDQ6649508
Publication date: 6 December 2024
completely integrable systemsLax pairsHamiltonian structuresBäcklund and auto-Bäcklund transformationsPainlevé equations and hierarchies
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Painlevé-type functions (33E17)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonisospectral scattering problems and similarity reductions
- On matrix Painlevé hierarchies
- Bäcklund transformations for a matrix second Painlevé equation
- A new derivation of Painlevé hierarchies
- Geometry of the string equations
- On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy
- Factorisation of energy dependent Schrödinger operators: Miura maps and modified systems
- Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent
- Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- Coupled KdV equations with multi-Hamiltonian structures
- Monodromy- and spectrum-preserving deformations. I
- On the Bäcklund transformation for the Gel'fand-Dickey equations
- Nonlinear evolution equations associated with energy-dependent Schrödinger potentials
- Integrable evolution equations on associative algebras
- On non-isospectral flows, Painlevé equations, and symmetries of differential and difference equations
- Sur les équations différentielles du troisième ordre et d'ordre supérieur dont líntégrale générale a ses points critiques fixes.
- On a generalized \(2+1\) dispersive water wave hierarchy
- Coalescence limits for higher order Painlevé equations
- On the nesting of Painlevé hierarchies: a Hamiltonian approach
- Uniformization and transcendence of solutions for the first and second Painlevé hierarchies
- On the Painlevé test for non-abelian equations
- Non-autonomous Hénon-Heiles systems
- The first and second Painlevé equations of higher order and some relations between them
- On an extended second Painlevé hierarchy
- Bäcklund transformation of matrix equations and a discrete matrix first Painlevé equation
- Solution classes of the matrix second Painlevé hierarchy
- On matrix fourth Painlevé hierarchies
- The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases
- Bäcklund transformations for new fourth Painlevé hierarchies
- Integration via modification: a method of reduction of order for systems of ordinary differential equations
- WKB analysis of higher order Painlevé equations with a large parameter -- local reduction of 0-parameter solutions for Painlevé hierarchies \((P_{J})\) (\(J=\text{ I, II-1 or II-2}\))
- Mathematics of dispersive water waves
- Bäcklund transformations for fourth Painlevé hierarchies
- Painlevé hierarchies and the Painlevé test
- On the extension of inverse scattering method.
- A Higher-Order Water-Wave Equation and the Method for Solving It
- Finding Eigenvalue Problems for Solving Nonlinear Evolution Equations
- Classification of Integrable One-Component Systems on Associative Algebras
- Noncommutative Toda chains, Hankel quasideterminants and the Painlevé II equation
- Noncommutative Korteweg–de Vries and modified Korteweg–de Vries hierarchies via recursion methods
- String theory and water waves
- Non-isospectral lattice hierarchies in 2 + 1 dimensions and generalized discrete Painlevé hierarchies
- A nonisospectral extension of the Volterra hierarchy to 2+1 dimensions
- Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems
- Non-isospectral deformations and Darboux transformations for the third-order spectral problem
- Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1
- The Symmetric Fourth Painlevé Hierarchy and Associated Special Polynomials
- Bäcklund transformations for a discrete second Painlevé hierarchy
- The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations
- Generalised KdV and MKdV equations associated with symmetric spaces
- Rational solutions for Schwarzian integrable hierarchies
- Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations
- The bi-Hamiltonian structure of some nonlinear fifth- and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants
- On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
- Energy-dependent third-order Lax operators
- Approximate equations for long water waves
- Almost Periodic Solutions of the KdV Equation
- Evolution equations possessing infinitely many symmetries
- A simple model of the integrable Hamiltonian equation
- Bäcklund transformations for the second Painlevé hierarchy: a modified truncation approach
- The discrete first, second and thirty-fourth Painlevé hierarchies
- Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
- On a new non-isospectral variant of the Boussinesq hierarchy
- Nonisospectral scattering problems: A key to integrable hierarchies
- On construction of recursion operators from Lax representation
- Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
- Amalgamations of the Painlevé equations
- Bäcklund Transformations and Solution Hierarchies for the Fourth Painlevé Equation
- Hierarchies of Difference Equations and Bäcklund Transformations
- The Hamiltonian structure of the second Painlevé hierarchy
- Linear problems and hierarchies of Painlevé equations
- Rational Solutions of Painlevé Equations
Related Items (1)
This page was built for publication: Higher-order nonlinear special functions: Painlevé hierarchies, a survey
