Nonlinearity, ISSN 1361-6544, 2017, Volume 30, Issue 7, pp. 2982 - 3009

We consider the second Painleve equation u'' (x) = 2u(3)(x) + xu(x) - alpha, where alpha is a nonzero constant. Using the Deift-Zhou nonlinear steepest descent...

connection formulas | Riemann-Hilbert problem | Painlevé II equation | POLYNOMIALS | MATHEMATICS, APPLIED | RESPECT | Painleve II equation | UNIFORM ASYMPTOTICS | PHYSICS, MATHEMATICAL

connection formulas | Riemann-Hilbert problem | Painlevé II equation | POLYNOMIALS | MATHEMATICS, APPLIED | RESPECT | Painleve II equation | UNIFORM ASYMPTOTICS | PHYSICS, MATHEMATICAL

Journal Article

Advances in Mathematics, ISSN 0001-8708, 03/2017, Volume 309, pp. 155 - 208

We study a model of nonintersecting Brownian bridges on an interval with either absorbing or reflecting walls at the boundaries, focusing on the point in...

Determinantal processes | Hard-edge tacnode process | Hard-edge Pearcey process | Schlesinger transformation | Nonintersecting Brownian motions | Painlevé II | Painleve II | RANDOM-MATRIX THEORY | MOTIONS | MATHEMATICS | PEARCEY PROCESS | GROWTH | GAP | TACNODE PROCESS | EQUATION | Trucks | Analysis | Four-wheel drive

Determinantal processes | Hard-edge tacnode process | Hard-edge Pearcey process | Schlesinger transformation | Nonintersecting Brownian motions | Painlevé II | Painleve II | RANDOM-MATRIX THEORY | MOTIONS | MATHEMATICS | PEARCEY PROCESS | GROWTH | GAP | TACNODE PROCESS | EQUATION | Trucks | Analysis | Four-wheel drive

Journal Article

Meccanica, ISSN 0025-6455, 12/2017, Volume 52, Issue 15, pp. 3531 - 3540

Stefan-type moving boundary problems are investigated for an extended Dym equation originally introduced in work of Camassa and Holm. Reduction is made to an...

Classical Mechanics | Civil Engineering | Automotive Engineering | Moving boundary | Dym | Mechanical Engineering | Painlevé II | Physics | 37K10 | MECHANICS | EXPLICIT SOLUTIONS | EVOLUTION | Painleve II | BACKLUND-TRANSFORMATIONS | SOLITON

Classical Mechanics | Civil Engineering | Automotive Engineering | Moving boundary | Dym | Mechanical Engineering | Painlevé II | Physics | 37K10 | MECHANICS | EXPLICIT SOLUTIONS | EVOLUTION | Painleve II | BACKLUND-TRANSFORMATIONS | SOLITON

Journal Article

Random Matrices: Theory and Application, ISSN 2010-3263, 10/2018, Volume 7, Issue 4

We consider the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painleve. II equation u ''(x) = 2u(3)(x) + xu(x) - alpha for...

Hastings-McLeod solutions | Ablowitz-Segur solutions | Bäcklund transformation | Painlevé II equation | Painleve II equation | STATISTICS & PROBABILITY | ASYMPTOTICS | Backlund transformation | PHYSICS, MATHEMATICAL

Hastings-McLeod solutions | Ablowitz-Segur solutions | Bäcklund transformation | Painlevé II equation | Painleve II equation | STATISTICS & PROBABILITY | ASYMPTOTICS | Backlund transformation | PHYSICS, MATHEMATICAL

Journal Article

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2016, Volume 76, Issue 6, pp. 2286 - 2305

The equations governing one-dimensional, steady-state electrodiffusion are considered when there are arbitrarily many mobile ionic species present, in any...

Electrodiffusion | Ionic transport | PainlevéII | Liquid junctions | Goldman-Hodgkin-Katz formulas | MATHEMATICS, APPLIED | Painleve II | STEADY ELECTROLYSIS | ELECTRICAL STRUCTURES | ION-TRANSPORT | electrodiffusion | SLIP | MEMBRANES | Goldman Hodgkin Katz formulas | 3RD-ORDER | ASSUMPTION | INTERFACES | PAINLEVE II MODEL | liquid junctions | ionic transport

Electrodiffusion | Ionic transport | PainlevéII | Liquid junctions | Goldman-Hodgkin-Katz formulas | MATHEMATICS, APPLIED | Painleve II | STEADY ELECTROLYSIS | ELECTRICAL STRUCTURES | ION-TRANSPORT | electrodiffusion | SLIP | MEMBRANES | Goldman Hodgkin Katz formulas | 3RD-ORDER | ASSUMPTION | INTERFACES | PAINLEVE II MODEL | liquid junctions | ionic transport

Journal Article

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Hankel Determinant Approach to Generalized Vorob’ev–Yablonski Polynomials and Their Roots

Constructive Approximation, ISSN 0176-4276, 12/2016, Volume 44, Issue 3, pp. 417 - 453

Generalized Vorob’ev–Yablonski polynomials have been introduced by Clarkson and Mansfield in their study of rational solutions of the second Painlevé...

34M50 | Secondary 35Q53 | Numerical Analysis | Analysis | Primary 34M55 | Schur functions | Mathematics | Vorob’ev–Yablonski polynomials | KdV and Painlevé II hierarchy | Hankel determinant representation | MATHEMATICS | KdV and Painleve II hierarchy | BEHAVIOR | Vorob'ev-Yablonski polynomials | LARGE-DEGREE ASYMPTOTICS | EQUATION

34M50 | Secondary 35Q53 | Numerical Analysis | Analysis | Primary 34M55 | Schur functions | Mathematics | Vorob’ev–Yablonski polynomials | KdV and Painlevé II hierarchy | Hankel determinant representation | MATHEMATICS | KdV and Painleve II hierarchy | BEHAVIOR | Vorob'ev-Yablonski polynomials | LARGE-DEGREE ASYMPTOTICS | EQUATION

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 5/2012, Volume 147, Issue 3, pp. 582 - 622

We study the distribution of the maximal height of the outermost path in the model of N nonintersecting Brownian motions on the half-line as N→∞, showing that...

Brownian excursions | Random matrix theory | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Airy process | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Painlevé II | Discrete orthogonal polynomials | Physics | UNIVERSALITY | Painleve II | DOUBLE SCALING LIMIT | AIRY-KERNEL | DETERMINANT | PHYSICS, MATHEMATICAL | RANDOM-MATRIX MODEL | ASYMPTOTICS | LEVEL-SPACING DISTRIBUTIONS | EQUATION | Toy industry | Analysis

Brownian excursions | Random matrix theory | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Airy process | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Painlevé II | Discrete orthogonal polynomials | Physics | UNIVERSALITY | Painleve II | DOUBLE SCALING LIMIT | AIRY-KERNEL | DETERMINANT | PHYSICS, MATHEMATICAL | RANDOM-MATRIX MODEL | ASYMPTOTICS | LEVEL-SPACING DISTRIBUTIONS | EQUATION | Toy industry | Analysis

Journal Article

Communications in mathematical physics, ISSN 1432-0916, 2017, Volume 359, Issue 1, pp. 223 - 263

We analyze the left-tail asymptotics of deformed Tracy–Widom distribution functions describing the fluctuations of the largest eigenvalue in invariant random...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | RANDOM PERMUTATIONS | HANKEL DETERMINANT | SPACING DISTRIBUTIONS | INVERSE SCATTERING | BULK SCALING LIMIT | RANDOM-MATRIX THEORY | SINE KERNEL | ORTHOGONAL POLYNOMIALS | FREDHOLM DETERMINANT | PHYSICS, MATHEMATICAL | PAINLEVE-II | Analysis | Distribution (Probability theory)

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | RANDOM PERMUTATIONS | HANKEL DETERMINANT | SPACING DISTRIBUTIONS | INVERSE SCATTERING | BULK SCALING LIMIT | RANDOM-MATRIX THEORY | SINE KERNEL | ORTHOGONAL POLYNOMIALS | FREDHOLM DETERMINANT | PHYSICS, MATHEMATICAL | PAINLEVE-II | Analysis | Distribution (Probability theory)

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 03/2017, Volume 13

A class of nonlinear Schrodinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction...

Korteweg-type capillary system | Painlevé capillarity | Ermakov–Painlevé II equation | Bäcklund transformation | Ermakov-Painleve II equation | type capillary system | BEAMS | 2ND | MODEL | NONLINEAR SCHRODINGER-EQUATION | LARGE-DEGREE ASYMPTOTICS | PHYSICS, MATHEMATICAL | WAVES | SOLITONS | Backlund transformation | Korteweg | TRANSCENDENT | Painleve capillarity | TRANSFORMATIONS | MADELUNG | Functions (mathematics) | Reduction | Nonlinear equations | Transformations (mathematics) | Mathematical analysis | Capillarity | Schroedinger equation | Free energy | Symmetry

Korteweg-type capillary system | Painlevé capillarity | Ermakov–Painlevé II equation | Bäcklund transformation | Ermakov-Painleve II equation | type capillary system | BEAMS | 2ND | MODEL | NONLINEAR SCHRODINGER-EQUATION | LARGE-DEGREE ASYMPTOTICS | PHYSICS, MATHEMATICAL | WAVES | SOLITONS | Backlund transformation | Korteweg | TRANSCENDENT | Painleve capillarity | TRANSFORMATIONS | MADELUNG | Functions (mathematics) | Reduction | Nonlinear equations | Transformations (mathematics) | Mathematical analysis | Capillarity | Schroedinger equation | Free energy | Symmetry

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 10/2011, Volume 64, Issue 10, pp. 1305 - 1383

We study a model of n one‐dimensional, nonintersecting Brownian motions with two prescribed starting points at time t = 0 and two prescribed ending points at...

MATHEMATICS | GAUSSIAN RANDOM MATRICES | UNIVERSALITY | MATHEMATICS, APPLIED | DOUBLE SCALING LIMIT | EXTERNAL SOURCE | DETERMINANTAL PROCESSES | RIEMANN-HILBERT PROBLEM | ASYMPTOTICS | LARGE N LIMIT | MULTIPLE ORTHOGONAL POLYNOMIALS | PAINLEVE-II

MATHEMATICS | GAUSSIAN RANDOM MATRICES | UNIVERSALITY | MATHEMATICS, APPLIED | DOUBLE SCALING LIMIT | EXTERNAL SOURCE | DETERMINANTAL PROCESSES | RIEMANN-HILBERT PROBLEM | ASYMPTOTICS | LARGE N LIMIT | MULTIPLE ORTHOGONAL POLYNOMIALS | PAINLEVE-II

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2015, Volume 309, pp. 108 - 118

The six Painlevé equations were first formulated about a century ago. Since the 1970s, it has become increasingly recognized that they play a fundamental role...

Tronquée solutions | Ablowitz–Segur solutions | Imaginary Painlevé II | Pole field solver | Modified Painlevé II | Ablowitz-Segur solutions | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | Modified Painleve II | Tronquee solutions | Imaginary Painleve II | PHYSICS, MATHEMATICAL

Tronquée solutions | Ablowitz–Segur solutions | Imaginary Painlevé II | Pole field solver | Modified Painlevé II | Ablowitz-Segur solutions | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | Modified Painleve II | Tronquee solutions | Imaginary Painleve II | PHYSICS, MATHEMATICAL

Journal Article

Symmetry, integrability and geometry, methods and applications, ISSN 1815-0659, 2018, Volume 14

The increasing tritronquee solutions of the Painleve-II equation with parameter a exhibit square-root asymptotics in the maximally-large sector larg sector...

UNIVERSALITY | tronquee solutions | CATASTROPHE | Painleve-II equation | LIMIT | CRITICAL-BEHAVIOR | NONLINEAR SCHRODINGER-EQUATION | LARGE-DEGREE ASYMPTOTICS | PHYSICS, MATHEMATICAL | Poles | Parameters | Asymptotic properties | Integrals

UNIVERSALITY | tronquee solutions | CATASTROPHE | Painleve-II equation | LIMIT | CRITICAL-BEHAVIOR | NONLINEAR SCHRODINGER-EQUATION | LARGE-DEGREE ASYMPTOTICS | PHYSICS, MATHEMATICAL | Poles | Parameters | Asymptotic properties | Integrals

Journal Article

Constructive Approximation, ISSN 0176-4276, 2/2014, Volume 39, Issue 1, pp. 197 - 222

The tacnode Riemann–Hilbert problem is a 4×4 matrix-valued RH problem that appears in the description of the local behavior of two touching groups of...

Tacnode | 34M50 | 60J65 | Two-matrix model | Mathematics | 34M55 | 33E17 | Primary 30E20 | Painlevé II equation | Numerical Analysis | Analysis | Secondary 15B52 | Integral representation | Hastings-McLeod solution | Riemann–Hilbert problem | Riemann-Hilbert problem | 2-MATRIX MODEL | MATHEMATICS | BROWNIAN MOTIONS | MATRICES | Painleve II equation | CRITICAL-BEHAVIOR | Trucks | Four-wheel drive

Tacnode | 34M50 | 60J65 | Two-matrix model | Mathematics | 34M55 | 33E17 | Primary 30E20 | Painlevé II equation | Numerical Analysis | Analysis | Secondary 15B52 | Integral representation | Hastings-McLeod solution | Riemann–Hilbert problem | Riemann-Hilbert problem | 2-MATRIX MODEL | MATHEMATICS | BROWNIAN MOTIONS | MATRICES | Painleve II equation | CRITICAL-BEHAVIOR | Trucks | Four-wheel drive

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2018, Volume 50, Issue 2, pp. 2233 - 2279

We study the Fredholm determinant of an integrable operator acting on the interval (0, s) whose kernel is constructed out of the Psi-function associated with a...

Unitary ensembles | Riemann-Hilbert problem | Gap probability | Painlevécoupled painlevéequations | Deift-Zhou steepest descent analysis | Singular potentials | Asymptotics | MATHEMATICS, APPLIED | INVERSE SCATTERING | unitary ensembles | STRONG ASYMPTOTICS | gap probability | TIME-DELAY MATRIX | BESSEL KERNEL | RIEMANN-HILBERT APPROACH | singular potentials | MODELS | Deift Zhou steepest descent analysis | asymptotics | ORTHOGONAL POLYNOMIALS | LEVEL-SPACING DISTRIBUTIONS | FREDHOLM DETERMINANTS | Painleve and coupled Painleve equations | Riemann Hilbert problem | PAINLEVE-II

Unitary ensembles | Riemann-Hilbert problem | Gap probability | Painlevécoupled painlevéequations | Deift-Zhou steepest descent analysis | Singular potentials | Asymptotics | MATHEMATICS, APPLIED | INVERSE SCATTERING | unitary ensembles | STRONG ASYMPTOTICS | gap probability | TIME-DELAY MATRIX | BESSEL KERNEL | RIEMANN-HILBERT APPROACH | singular potentials | MODELS | Deift Zhou steepest descent analysis | asymptotics | ORTHOGONAL POLYNOMIALS | LEVEL-SPACING DISTRIBUTIONS | FREDHOLM DETERMINANTS | Painleve and coupled Painleve equations | Riemann Hilbert problem | PAINLEVE-II

Journal Article

Asymptotic Analysis, ISSN 0921-7134, 2011, Volume 73, Issue 1-2, pp. 53 - 96

We study non-linear ground states of the Gross-Pitaevskii equation in the space of one, two and three dimensions with a radially symmetric harmonic potential....

Painlevé II | Bose-Einstein | Thomas-Fermi | ground state | hydrodynamics limit | Gross-Pitaevskii equation | EIGENVALUES | MATHEMATICS, APPLIED | Painleve II | BOSE-EINSTEIN CONDENSATE | VORTEX | SCHRODINGER-OPERATORS

Painlevé II | Bose-Einstein | Thomas-Fermi | ground state | hydrodynamics limit | Gross-Pitaevskii equation | EIGENVALUES | MATHEMATICS, APPLIED | Painleve II | BOSE-EINSTEIN CONDENSATE | VORTEX | SCHRODINGER-OPERATORS

Journal Article

16.
Full Text
Limit Theorems for Height Fluctuations in a Class of Discrete Space and Time Growth Models

Journal of Statistical Physics, ISSN 0022-4715, 3/2001, Volume 102, Issue 5, pp. 1085 - 1132

We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function ht(x) with corner initialization....

shape fluctuations | Mathematical and Computational Physics | invariance principle | growth processes | Quantum Physics | digital boiling | limit theorems | Physics | saddle point analysis | Physical Chemistry | Airy kernel | random matrix theory | Painlevé II | Statistical Physics | Random matrix theory | Saddle point analysis | Growth processes | Invariance principle | Limit theorems | Shape fluctuations | Digital boiling | LONGEST INCREASING SUBSEQUENCES | Painleve II | PHYSICS, MATHEMATICAL | Airy Kernel | RANDOM MATRICES | DISTRIBUTIONS | PERMUTATIONS | ASYMPTOTICS

shape fluctuations | Mathematical and Computational Physics | invariance principle | growth processes | Quantum Physics | digital boiling | limit theorems | Physics | saddle point analysis | Physical Chemistry | Airy kernel | random matrix theory | Painlevé II | Statistical Physics | Random matrix theory | Saddle point analysis | Growth processes | Invariance principle | Limit theorems | Shape fluctuations | Digital boiling | LONGEST INCREASING SUBSEQUENCES | Painleve II | PHYSICS, MATHEMATICAL | Airy Kernel | RANDOM MATRICES | DISTRIBUTIONS | PERMUTATIONS | ASYMPTOTICS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 12/2013, Volume 324, Issue 3, pp. 715 - 766

The squared Bessel process is a 1-dimensional diffusion process related to the squared norm of a higher dimensional Brownian motion. We study a model of n...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | INVERSE SCATTERING | BROWNIAN MOTIONS | RIEMANN-HILBERT PROBLEM | WEIGHTS | ASYMPTOTICS | PHYSICS, MATHEMATICAL | EQUATION | MULTIPLE ORTHOGONAL POLYNOMIALS | PAINLEVE-II

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | INVERSE SCATTERING | BROWNIAN MOTIONS | RIEMANN-HILBERT PROBLEM | WEIGHTS | ASYMPTOTICS | PHYSICS, MATHEMATICAL | EQUATION | MULTIPLE ORTHOGONAL POLYNOMIALS | PAINLEVE-II

Journal Article

Nuclear Physics, Section B, ISSN 0550-3213, 2012, Volume 855, Issue 1, pp. 46 - 81

We study Stokes phenomena of the k × k isomonodromy systems with an arbitrary Poincaré index r, especially which correspond to the fractional-superstring (or...

FUSION RULES | LOOP EQUATIONS | FIELD-THEORIES | RATIONAL THEORIES | ISING-MODEL | MATRIX MODELS | SUPER-LIOUVILLE THEORY | PAINLEVE-II | 2D GRAVITY | BETHE-ANSATZ | PHYSICS, PARTICLES & FIELDS

FUSION RULES | LOOP EQUATIONS | FIELD-THEORIES | RATIONAL THEORIES | ISING-MODEL | MATRIX MODELS | SUPER-LIOUVILLE THEORY | PAINLEVE-II | 2D GRAVITY | BETHE-ANSATZ | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 10/2010, Volume 43, Issue 43, p. 434031

The Ward ansatze in twistor theory generate solutions of the SL(2, C) anti-self-dual Yang-Mills equations from solutions of the wave equation in spacetime. The...

YANG-MILLS EQUATION | GARNIER SYSTEMS | GENERAL-THEORY | PHYSICS, MULTIDISCIPLINARY | CLASSICAL-SOLUTIONS | PHYSICS, MATHEMATICAL | DEFORMATION | PAINLEVE-II

YANG-MILLS EQUATION | GARNIER SYSTEMS | GENERAL-THEORY | PHYSICS, MULTIDISCIPLINARY | CLASSICAL-SOLUTIONS | PHYSICS, MATHEMATICAL | DEFORMATION | PAINLEVE-II

Journal Article

Nonlinearity, ISSN 0951-7715, 04/2009, Volume 22, Issue 4, pp. 871 - 887

Ultra-discrete equations are equations in which both the dependent and independent variables can be restricted to take only integer values. In this paper, we...

MATHEMATICS, APPLIED | CELLULAR-AUTOMATA | PAINLEVE-II EQUATION | PHYSICS, MATHEMATICAL

MATHEMATICS, APPLIED | CELLULAR-AUTOMATA | PAINLEVE-II EQUATION | PHYSICS, MATHEMATICAL

Journal Article

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