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Algebraic and analytic aspects of integrable systems and painleve equations / [edited by] Anton Dzhamay, Kenichi Maruno and Christopher M. Ormerod.

By: Contributor(s): Material type: TextTextSeries: Contemporary mathematics ; 651Publication details: Providence : American Mathematical Society, 2015.Description: xi, 194 p. : illustrations ; 26 cmISBN:
  • 9781470416546 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512c
Contents:
Pade Interpolation and Hypergeometric Series / Masatoshi Noumi -- A q-analogue of the Drinfeld-Sokolov Hierarchy of Type A and q-Painleve system / Takao Suzuki -- Fractional Calculus of Quantum Painleve 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.
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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512c (Browse shelf(Opens below)) Available 136701
Total holds: 0

Includes bibliographical references.

Pade Interpolation and Hypergeometric Series / Masatoshi Noumi --
A q-analogue of the Drinfeld-Sokolov Hierarchy of Type A and q-Painleve system / Takao Suzuki --
Fractional Calculus of Quantum Painleve 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.

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.

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