- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painleve 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 Painleve 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
Pade interpolation and hypergeometric series by M. Noumi
A $q$-analogue of the Drinfeld-Sokolov hierarchy of type $A$ and $q$-Painleve system by T. Suzuki
Fractional calculus of quantum Painleve systems of type $A^{(1)}_1$ by H. Nagoya
Spectral curves and discrete Painleve equations by C. M. Ormerod
Geometric analysis of reductions from Schlesinger transformations to difference Painleve equations by A. Dzhamay and T. Takenawa
Beta ensembles, quantum Painleve equations and isomonodromy systems by I. Rumanov
Inverse scattering transform for the focusing nonlinear Schrodinger equation with a one-sided non-zero boundary condition by B. Prinari and F. Vitale
