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Algebraic and analytic aspects of integrable systems and painlevé equations : AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, January 18, 2014, Baltimore, Maryland / Anton Dzhamay, Kenichi Maruno, Christopher M. Ormerod, editors.

Publication:
Providence, Rhode Island : American Mathematical Society, [2015]
Conference Name:
AMS Special Session, Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations (2014 : Baltimore, Md.)
Series:
Contemporary mathematics (American Mathematical Society) ; v. 651.
Contemporary mathematics ; 651
Format/Description:
Conference/Event
Book
xi, 194 pages ; 26 cm.
Subjects:
Painlevé equations -- Congresses.
Algebra -- Congresses.
Ordinary differential equations -- Differential equations in the complex domain -- Painlevé and other special equations; classification, hierarchies;.
Ordinary differential equations -- Differential equations in the complex domain -- Isomonodromic deformations.
Dynamical systems and ergodic theory -- Infinite-dimensional Hamiltonian systems -- Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.).
Difference and functional equations -- Difference equations -- Difference equations, additive.
Partial differential equations -- Equations of mathematical physics and other areas of application -- NLS-like equations (nonlinear Schrödinger).
Algebraic geometry -- Birational geometry -- Birational automorphisms, Cremona group and generalizations.
Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Applications to integrable systems.
Special functions (33-XX deals with the properties of functions as functions) -- Hypergeometric functions -- Generalized hypergeometric series, $.
Approximations and expansions -- Approximations and expansions -- Interpolation.
Quantum theory -- Groups and algebras in quantum theory -- Relations with integrable systems.
Algebra.
Painlevé equations.
Form/Genre:
Conference papers and proceedings.
Summary:
This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD. The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory. Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painlevé equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.
Contents:
Padé Interpolation and Hypergeometric Series / Masatoshi Noumi
A q-analogue of the Drinfeld-Sokolov Hierarchy of Type A and q-Painlevé system / Takao Suzuki
Fractional Calculus of Quantum Painlevé Systems of Type Al(1) / Hajime Nagoya
Spectral Curves and Discrete Painlevé Equations / Christopher M. Ormerod
Geometric Analysis of Reductions from Schlesinger Transformations to Difference Painlevé Equations / Anton Dzhamay and Tomoyuki Takenawa
Beta Ensembles, Quantum Painlevé Equations and Isomonodromy Systems / Igor Rumanov
Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation with a One-Sided Non-Zero Boundary Condition / B. Prinari and F. Vitale.
Notes:
Includes bibliographical references.
Contributor:
Dzhamay, Anton, 1970- editor.
Maruno, Ken'ichi, 1971- editor.
Ormerod, Christopher M., 1982- editor.
ISBN:
9781470416546
1470416549
OCLC:
907132792
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