Integrable And Superintegrable Systems

Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.

Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's. Contents:The Main Soliton Theorem (I Cherednik)Functional Bethe Ansatz (E K Sklyanin)Integrability in Models of Two-Dimensional Turbulence (Y Murometz & S Razboynick)Solitons, Numerical Chaos and Cellular Automata (M J Ablowitz et al.)The Unstable Nonlinear Schrödinger Equation (T Yajima & M Wadati)Classification of Integrable Equations (R K Dodd)List of All Integrable Hamiltonian Systems of General Type with Two Degrees of Freedom (A T Fomenko)Finite-Dimensional Soliton Systems (S N M Ruijsenaars)Relativistic Analogs of Basic Integrable Systems (J Gibbons & B A Kupershmidt)Liouville Generating Functions for Isospectral Flows in Loop Algebras (M R Adams et al.)A Loop Algebra Decomposition for Korteweg-de Vries Equations (R J Schilling)Energy Dependent Spectral Problems: Their Hamiltonian Structures and Miura Maps (A P Fordy)Commuting Differential Operators Over Integrable Hierarchies (F Guil)Lie Superalgebra Structure on Eigenfunctions, and Jets of the Resolvent's Kernal Near the Derivative and the Bott Cocycle (A O Radul)Super Miura Transformations, Super Schwarzian Derivatives and Super Hill Operators (P Mathieu) Readership: Mathematicians and physicists. keywords:

The volume is suitable for graduate students and research mathematicians interested in integrable systems.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day. that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hennit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day. that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hennit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This title is based on the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathematiques in Montreal (Quebec).

Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This proceedings volume grew out of the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathématiques in Montréal (Quebec). The meeting brought together scientists working in the area of finite-dimensional integrable systems to discuss new developments in this active field of interest. Properties possessed by these systems are manifold. In classical mechanics, they.

Proceedings of the NATO Advanced Research Workshop, held in Cadiz, Spain, from 12 to 16 June 2002