Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II

From MaRDI portal
Publication:995020

DOI10.1016/0167-2789(81)90021-XzbMath1194.34166OpenAlexW2501592988MaRDI QIDQ995020

Michio Jimbo, Tetsuji Miwa

Publication date: 13 September 2010

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(81)90021-x



Related Items

Fredholm determinants, differential equations and matrix models, Classical conformal blocks and Painlevé VI, Isomonodromy, Painlevé transcendents and scattering off of black holes, Three-parameter solutions of the PV Schlesinger-type equation near the point at infinity and the monodromy data, Linear integral equations and nonlinear difference-difference equations, Painlevé V and the Hankel determinant for a singularly perturbed Jacobi weight, Painlevé property of monodromy preserving deformation equations and the analyticity of \(\tau\) functions, Classifying (almost)-Belyi maps with five exceptional points, Computation of \(RS\)-pullback transformations for algebraic Painlevé VI solutions, Hypergeometric \(\tau\) functions of the \(q\)-Painlevé systems of types \(A_4^{(1)}\) and \((A_1+A_1')^{(1)}\), Singular instantons and Painlevé VI, A note on the averaging for single-phase elliptic solutions of the Toda and the Volterra lattices, Dual isomonodromic deformations and moment maps to loop algebras, Classical conformal blocks and accessory parameters from isomonodromic deformations, Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\), Connection formulae for Painlevé V functions, Moduli spaces of \(d\)-connections and difference Painlevé equations, Connection formulae for Painlevé V functions. II: the \(\delta\) function Bose gas problem, Construction and classification of certain algebraic solutions of Garnier systems, Bihamiltonian cohomologies and integrable hierarchies. II: The tau structures, Duality for the general isomonodromy problem, Recursion operators and bi-Hamiltonian structures in multidimensions. I, Parametric Painlevé equations, Integrable differential systems of topological type and reconstruction by the topological recursion, Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations, Rational solutions of the Painlevé-II equation revisited, On some special solutions of the fifth Painlevé equation, On connection formulas for asymptotic expansions for some special solutions of the fifth Painlevé equation, From the Darboux-Egorov system to bi-flat \(F\)-manifolds, Second-degree Painlevé equations and their contiguity relations, Painlevé V and a Pollaczek-Jacobi type orthogonal polynomials, A variation of the \(q\)-Painlevé system with affine Weyl group symmetry of type \(E_7^{(1)}\), On linear systems and \(\tau\) functions associated with Lamé's equation and Painlevé's equation VI, The dependence on the monodromy data of the isomonodromic tau function, Isomonodromic deformations and twisted Yangians arising in Teichmüller theory, Quantum curve and the first Painlevé equation, Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary, Remarks on the Yablonskii-Vorob'ev polynomials, Discrete gap probabilities and discrete Painlevé equations., Two-point correlation functions of scaling fields in the Dirac theory on the Poincaré disk, Painlevé equations and complex reflections., Isomonodromic deformations of connections with singularities of parahoric formal type, An area-preserving action of the modular group on cubic surfaces and the Painlevé VI equation, Painlevé property and geometry, The global parametrix in the Riemann-Hilbert steepest descent analysis for orthogonal polynomials, The Hilbert series of \(\mathcal{N}=1\) \(SO(N_c)\) and \(Sp(N_c)\) SQCD, Painlevé VI and integrable systems, Apparent singularities of Fuchsian equations and the Painlevé property for Garnier systems, Modifications of bundles, elliptic integrable systems, and related problems, Landau-Lifshitz equation, uniaxial anisotropy case: theory of exact solutions, Quantum Painlevé equations: from continuous to discrete and back, A matrix model for the topological string. I: Deriving the matrix model, The master Painlevé VI heat equation, Gap probabilities for the generalized Bessel process: a Riemann-Hilbert approach, Stokes phenomena and non-perturbative completion in the multi-cut two-matrix models, Stokes phenomena and quantum integrability in non-critical string/M theory, Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation, The relationship between semiclassical Laguerre polynomials and the fourth Painlevé equation, On the Painlevé property of isomonodromic deformations of Fuchsian systems, The sixth Painlevé transcendents and the associated Schlesinger equation, Rational solutions of nonlinear evolution equations, vertex operators, and bispectrality, Justification of the asymptotic formulas obtained by the isomonodromic deformation method, Surfaces de Bonnet et équations de Painlevé, Matrix models of two-dimensional quantum gravity and isomonodromic solutions of ``discrete Painlevé equations, Turning points of linear systems and the double asymptotics of the Painlevé transcendents, Passage to the limit \(\mathbb{P}_ 2\longrightarrow\mathbb{P}_ 1\), Weakly nonlinear solutions of equation \(P^ 2_ 1\), Essential singularity of the second-genus Painlevé function and the nonlinear Stokes phenomenon, Hermite-Padé approximation, isomonodromic deformation and hypergeometric integral, Ermakov-Painlevé II symmetry reduction of a Korteweg capillarity system, The Kontsevich matrix integral: convergence to the Painlevé hierarchy and Stokes' phenomenon, The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem, Moduli spaces for linear differential equations and the Painlevé equations, On the Riemann-Hilbert-Birkhoff inverse monodromy problem associated with the third Painlevé equation, On complete integrability of a hierarchy of finite-dimensional Hamiltonian systems, The degeneration of the two dimensional Garnier system and the polynomial Hamiltonian structure, Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. III, Towards second order Lax pairs to discrete Painlevé equations of first degree, Discrete systems related to some equations of the Painlevé-Gambier classification, The Lamé family of connections on the projective line, Transformations of spherical blocks, Quantum Baxter-Belavin \(R\)-matrices and multidimensional Lax pairs for Painlevé VI, Special polynomials related to the supersymmetric eight-vertex model: a summary, Quadratic transformations for the sixth Painlevé equation, Isomonodromic deformations and SU\(_2\)-invariant instantons on \(S^4\), The Painlevé III, V and VI transcendents as solutions of the Einstein-Weyl equations, An initial-boundary value problem on the half-line for the MKdV equation, Vector perturbations of Kerr-\(\mathrm{AdS}_5\) and the Painlevé VI transcendent, Diagrams for nonabelian Hodge spaces on the affine line, Strominger-Yau-Zaslow geometry, affine spheres and Painlevé III, Bi-orthogonal systems on the unit circle, regular semi-classical weights and integrable systems. II, The asymptotic behavior of solutions of the sine-Gordon equation with singularities zero, A unified Hamiltonian system on polynomial bundles, and the structure of stationary problems, Geometry of the string equations, Functional realization of basic representations of factorizable Lie groups and algebras, Isomonodromic deformations and self-similar solutions for the Einstein- Maxwell equations, Liouville's theorem and the method of the inverse problem, On the structure of Painlevé transcendents with a large parameter, A new solution of the fourth Painlevé equation with a solvable monodromy, Studies on the Painlevé equations. III: Second and fourth Painlevé equations, \(P_{II}\) and \(P_{IV}\), Painlevé representation of Tracy-Widom\(_\beta\) distribution for \(\beta=6\), Painlevé equations -- nonlinear special functions., On a general singular solution of the fifth Painlevé equation along the positive real axis, Integrable systems and isomonodromy deformations, Rational \(so(3)\) Gaudin model with general boundary terms, Hamiltonians associated with the sixth Painlevé equation, Isomonodromy for the degenerate fifth Painlevé equation, Emptiness formation probability of the six-vertex model and the sixth Painlevé equation, Moduli of unramified irregular singular parabolic connections on a smooth projective curve, Open problems for Painlevé equations, Kerr scattering coefficients via isomonodromy, Limit relation between Toda chains and the elliptic \(\mathrm{SL}(N,\mathbb{C})\) top, Quantum spectral problems and isomonodromic deformations, The geometry of the Hermitian matrix model and lattices for the NLS and dNLS hierarchies, The sixth Painlevé equation as similarity reduction of \({\widehat{\mathfrak{gl}}_3}\) generalized Drinfel'd-Sokolov hierarchy, Higher-dimensional uniformisation and \(W\)-geometry, Bilinear structure and Schlesinger transforms of the \(q\)-P\(_{III}\) and \(q\)-P\(_{VI}\) equations, On the tau function of the hypergeometric equation, Correction to: ``The dependence on the monodromy data of the isomonodromic tau function, Painlevé 2 equation with arbitrary monodromy parameter, topological recursion and determinantal formulas, The space of monodromy data for the Jimbo-Sakai family of \(q\)-difference equations, Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy, Local moduli of semisimple Frobenius coalescent structures, Gravity, strings, modular and quasimodular forms, Teichmüller spaces as degenerated symplectic leaves in Dubrovin-Ugaglia Poisson manifolds, 2-parameter \(\tau\)-function for the first Painlevé equation: topological recursion and direct monodromy problem via exact WKB analysis, Gap probability of the circular unitary ensemble with a Fisher-Hartwig singularity and the coupled Painlevé V system, Regular flat structure and generalized Okubo system, Analytic properties of solutions to equations in the generalized hierarchy of the second Painlevé equation, Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant, Asymptotic gap probability distributions of the Gaussian unitary ensembles and Jacobi unitary ensembles, The PDEs of biorthogonal polynomials arising in the two-matrix model, Poles of Painlevé IV rationals and their distribution, Irregular Liouville correlators and connection formulae for Heun functions, A systematic study on matrix models for Chern-Simons-matter theories, On deformations of linear systems of differential equations and the Painlevé property, Quantised Painlevé monodromy manifolds, Sklyanin and Calabi-Yau algebras, Differential equations with meromorphic coefficients, Symmetries of quantum Lax equations for the Painlevé equations, On a novel \(q\)-discrete analogue of the Painlevé VI equation, Generalized scaling reductions and Painlevé hierarchies, Flat structure on the space of isomonodromic deformations, Tau functions and the twistor theory of integrable systems., Nonintersecting Brownian excursions, Algebro-geometric approach to an Okamoto transformation, the Painlevé VI and Schlesinger equations, Resolving singularities and monodromy reduction of Fuchsian connections, Schlesinger transformations for algebraic Painlevé VI solutions, Painlevé IV and the semi-classical Laguerre unitary ensembles with one jump discontinuities, Painlevé equations, topological type property and reconstruction by the topological recursion, Schlesinger transformations for elliptic isomonodromic deformations, Regge and Okamoto symmetries, Quantum representation of affine Weyl groups and associated quantum curves, On integrable Ermakov-Painlevé IV systems, On determinant expansions for Hankel operators, Tau-functions and monodromy symplectomorphisms, Noncommutative Painlevé equations and systems of Calogero type, Canonical structure and symmetries of the Schlesinger equations, Painlevé III' and the Hankel determinant generated by a singularly perturbed Gaussian weight, On the increasing tritronquée solutions of the Painlevé-II equation, Schlesinger transformations for discrete second Painlevé equation: d-\(P_{II}\), Asymptotics of integrals of some functions related to the degenerate third Painlevé equation, Huygens' principle, Dirac operators, and rational solutions of the AKNS hierarchy, Painlevé III and a singular linear statistics in Hermitian random matrix ensembles. I., The \(k\)-tacnode process, The singularity of Kontsevich's solution for \(QH^{*}(\mathbb C P^{2})\), A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants, On the Riemann-Hilbert problem for a \(q\)-difference Painlevé equation, Variations for some Painlevé equations, The twistor theory of Whitham hierarchy, Perturbed Hankel determinant, correlation functions and Painlevé equations, The sigma form of the second Painlevé hierarchy, Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane, A Riemann-Hilbert approach to the Heun equation, On \(q\)-isomonodromic deformations and \(q\)-Nekrasov functions, From Heun class equations to Painlevé equations, Determinant structure for \(\tau\)-function of holonomic deformation of linear differential equations, Asymptotics of determinants of Hankel matrices via non-linear difference equations, On solutions of the Schlesinger equation in the neigborhood of the Malgrange \(\Theta \)-divisor, Connection formulae for the first Painlevé transcendent in the complex domain, Commutation relations and discrete garnier systems, Deformations of the Zolotarev polynomials and Painlevé VI equations, Aspects of Hecke symmetry: anomalies, curves, and chazy equations, Auto-Bäcklund transformations and special integrals for differential-delay Painlevé hierarchies, The Padé interpolation method applied to additive difference Painlevé equations, Connection formulae for Painlevé functions, Some explicit results for the generalized emptiness formation probability of the six-vertex model, Kerr-De Sitter quasinormal modes via accessory parameter expansion, On the spectral properties of the Hilbert transform operator on multi-intervals, On the algebraic solutions of the Painlevé-III (\(\mathrm{D}_7\)) equation, Unfolding of the unramified irregular singular generalized isomonodromic deformation, Einstein-Weyl spaces and dispersionless Kadomtsev-Petviashvili equation from Painlevé I and II, The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI., Large-degree asymptotics of rational Painlevé-IV solutions by the isomonodromy method, Universality conjecture and results for a model of several coupled positive-definite matrices, New \(2\times 2\)-matrix linear problems for the Painlevé equations III, V, Classical-quantum correspondence and functional relations for Painlevé equations, A review of the sixth Painlevé equation, Asymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation, Stokes manifolds and cluster algebras, Null Kähler geometry and isomonodromic deformations, Riemann-Hilbert approach to gap probabilities for the Bessel process, Classical solutions of the degenerate fifth Painlevé equation, Asymptotics for a singularly perturbed GUE, Painlevé III, double-confluent Heun equations, and small eigenvalues, FROM KP/UC HIERARCHIES TO PAINLEVÉ EQUATIONS, On families of constrictions in model of overdamped Josephson junction and Painlevé 3 equation*, Relations between different Hamiltonian forms of the third Painlevé equation, The elliptic representation of the general Painlevé VI equation, Application of the τ‐function theory of Painlevé equations to random matrices: PV, PIII, the LUE, JUE, and CUE, Determinant structure of the rational solutions for the Painlevé II equation, Second and fourth Painlevé hierarchies and Jimbo-Miwa linear problems, New 2+1 dimensional nonisospectral Toda lattice hierarchy, PDEs SATISFIED BY EXTREME EIGENVALUES DISTRIBUTIONS OF GUE AND LUE, Zeros of the isomonodromic tau functions in constructive conformal mapping of polycircular arc domains: the n-vertex case, QUANTUM PAINLEVÉ SYSTEMS OF TYPE $A_{n-1}^{(1)}$ WITH HIGHER DEGREE LAX OPERATORS, Nonlinear eigenvalue problems for generalized Painlevé equations, Nonlinear eigenvalue problems, On matrix Painlevé-4 equations, Exact distribution of largest Schmidt eigenvalue for quantum entanglement, The Painlevé-Kowalevski and Poly-Painlevé Tests for Integrability, Application of theτ-function theory of Painlevé equations to random matrices:PVI, the JUE, CyUE, cJUE and scaled limits, Center of mass distribution of the Jacobi unitary ensembles: Painlevé V, asymptotic expansions, All Binomial‐Type Painlevé Equations of the Second Order and Degree Three or Higher, The Hankel determinant associated with a singularly perturbed Laguerre unitary ensemble, DISCRETE INTEGRABLE SYSTEMS ASSOCIATED WITH THE UNITARY MATRIX MODEL, The sine-law gap probability, Painlevé 5, and asymptotic expansion by the topological recursion, ELLIPTIC ASYMPTOTIC REPRESENTATION OF THE FIFTH PAINLEVÉ TRANSCENDENTS, Caustics in 1+1 integrable systems, Expectation values of twist fields and universal entanglement saturation of the free massive boson, Non-abelian Painlevé systems with generalized Okamoto integral, Moduli spaces for the fifth Painlevé equation, On a zero curvature problem related to the ZS–AKNS operator, A degenerate Gaussian weight connected with Painlevé equations and Heun equations, Generalized Bonnet surfaces and Lax pairs of PVI, Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit, Painlevé Classification of a Class of Differential Equations of the Second Order and Second Degree, A constructive proof for the Umemura polynomials of the third Painlevé equation, Painlevé V, Painlevé XXXIV and the degenerate Laguerre unitary ensemble, Analytic geometry of semisimple coalescent Frobenius structures, Discrete Painlevé equations from singularity patterns: The asymmetric trihomographic case, Lattice equations arising from discrete Painlevé systems: II. ${A}_{4}^{(1)}$ case, Single-user MIMO system, Painlevé transcendents, and double scaling, Genus one Belyi maps by quadratic correspondences, Geometric aspects of Painlevé equations, R-matrix construction of electromagnetic models for the Painlevé transcendents, On Some Hamiltonian Properties of the Isomonodromic Tau Functions, Unnamed Item, Higher‐Order Painlevé Equations in the Polynomial Class II: Bureau Symbol P1, Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: The sl2 case, Painlevé transcendents and the Hankel determinants generated by a discontinuous Gaussian weight, On the linearization of the Painlevé III–VI equations and reductions of the three-wave resonant system, Random matrix models, double-time Painlevé equations, and wireless relaying, ON A NOVEL CLASS OF INTEGRABLE ODEs RELATED TO THE PAINLEVÉ EQUATIONS, On Stokes Phenomena for the Alternate Discrete PI Equation, Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I, On the eigenvalues of the Chandrasekhar–Page angular equation, Asymptotics of Discrete Painlevé V transcendents via the Riemann–Hilbert Approach, Cubic and Quartic Transformations of the Sixth Painlevé Equation in Terms of Riemann–Hilbert Correspondence, Strongly asymmetric discrete Painlevé equations: The additive case, Painlevé equations and the middle convolution, A new two-parameter family of isomonodromic deformations over the five punctured sphere, Studies on monodromy preserving deformation of linear differential equations on elliptic curves, Ermakov-Painlevé II Reduction in Cold Plasma Physics. Application of a Bäcklund Transformation, Random words, Toeplitz determinants and integrable systems. II, The symplectic and twistor geometry of the general isomonodromic deformation problem, Three kinds of constraints of potential for KdV hierarchy, New contiguity relation of the sixth Painlevé equation from a truncation, Mixed moments of characteristic polynomials of random unitary matrices, On self-similar solutions of the vortex filament equation, A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions, Symplectic manifolds and isomonodromic deformations, Antiquantization, isomonodromy, and integrability, Painlevé Classification of All Semi linear Partial Differential Equations of the Second Order. I. Hyperbolic Equations in Two Independent Variables, On factorized Lax pairs for classical many-body integrable systems, The Jacobi polynomial ensemble and the Painlevé VI equation, τ-function of discrete isomonodromy transformations and probability, Painlevé IV Asymptotics for Orthogonal Polynomials with Respect to a Modified Laguerre Weight, A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI, Kernels and point processes associated with Whittaker functions, Two Lax systems for the Painlevé II Equation, and Two Related Kernels in Random Matrix Theory, Contiguity relations for linearisable systems of Gambier type, Bäcklund transformations for certain rational solutions of Painlevé VI, A Riemann–Hilbert approach to Painlevé IV, Note on algebro-geometric solutions to triangular Schlesinger systems, On the origins of Riemann–Hilbert problems in mathematics*, Gaussian unitary ensemble with jump discontinuities and the coupled Painlevé II and IV systems, Unnamed Item, Replica Field Theories, Painlevé Transcendents, and Exact Correlation Functions, Classical integrability for beta-ensembles and general Fokker-Planck equations, Monodromy preserving deformation of ramified solutions to (Δ−m2)u = 0, Asymptotics of the largest eigenvalue distribution of the Laguerre unitary ensemble, GAUGE THEORY AND WILD RAMIFICATION, Symmetries in the third Painlevé equation arising from the modified Pohlmeyer-Lund-Regge hierarchy, Universal structure and universal equations (PDE) for unitary ensembles, Painlevé IV, σ-form, and the deformed Hermite unitary ensembles, Quantum Painlevé-Calogero correspondence for Painlevé VI, Quantum Painlevé-Calogero correspondence, Determinant formulas for the five-vertex model, tt∗ Toda equations for surface defects in SYM and instanton counting for classical Lie groups, A fully noncommutative analog of the Painlevé IV equation and a structure of its solutions*, Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries, Systematic construction of nonautonomous Hamiltonian equations of Painlevé type. I. Frobenius integrability, Hankel determinants for a Gaussian weight with Fisher–Hartwig singularities and generalized Painlevé IV equation, From topological recursion to wave functions and PDEs quantizing hyperelliptic curves, Different linearizations of non-abelian second Painlevé systems and related monodromy surfaces, The sixth Painlevé equation as isomonodromy deformation of an irregular system: monodromy data, coalescing eigenvalues, locally holomorphic transcendents and Frobenius manifolds, On classification of non-abelian Painlevé type systems, On the Riemann–Hilbert approach to asymptotics of tronquée solutions of Painlevé I, Holomorphic projective connections on surfaces, Painlevé V and confluent Heun equations associated with a perturbed Gaussian unitary ensemble, Hamiltonian structure of rational isomonodromic deformation systems, Hankel determinant and orthogonal polynomials for a perturbed Gaussian weight: From finite n to large n asymptotics, A singular linear statistic for a perturbed LUE and the Hankel matrices, Painlevé IV, Chazy II, and asymptotics for recurrence coefficients of semi‐classical Laguerre polynomials and their Hankel determinants, Sine‐kernel determinant on two large intervals, Universal cusp scaling in random partitions, Blowups in BPS/CFT correspondence, and Painlevé VI, Painlevé-III monodromy maps under the \(D_6 \rightarrow D_8\) confluence and applications to the large-parameter asymptotics of rational solutions, Exactly solvable anharmonic oscillator, degenerate orthogonal polynomials and Painlevé II



Cites Work