Integrability

A.V. Mikhailov (auth.), Alexander V. Mikhailov (eds.)3540881107, 9783540881100, 9783540881117, 3540881115

This is a unique collection of lectures on integrability, intended for graduate students or anyone who would like to master the subject from scratch, and written by leading experts in the field including Fields Medallist Serge Novikov. Since integrable systems have found a wide range of applications in modern theoretical and mathematical physics, it is important to recognise integrable models and, ideally, to obtain a global picture of the integrable world. The main aims of the book are to present a variety of views on the definition of integrable systems; to develop methods and tests for integrability based on these definitions; and to uncover beautiful hidden structures associated with integrable equations.

Table of contents :
Front Matter….Pages I-XIII
Introduction….Pages 1-15
Symmetries of Differential Equations and the Problem of Integrability….Pages 19-88
Number Theory and the Symmetry Classification of Integrable Systems….Pages 89-118
Four Lectures: Discretization and Integrability. Discrete Spectral Symmetries….Pages 119-138
Symmetries of Spectral Problems….Pages 139-173
Normal Form and Solitons….Pages 175-214
Multiscale Expansion and Integrability of Dispersive Wave Equations….Pages 215-244
Painlevé Tests, Singularity Structure and Integrability….Pages 245-277
Hirota’s Bilinear Method and Its Connection with Integrability….Pages 279-314
Integrability of the Quantum XXZ Hamiltonian….Pages 315-323
Back Matter….Pages 325-339