Integrability / A.V. Mikhailov (ed.).

Includes bibliographical references and index.

Symmetries of differential equations and the problem of integrability / A.V. Mikhailov and V.V. Sokolov -- Number theory and the symmetry classification of integrable systems / J.A. Sanders and J.P. Wang -- Four lectures : discretization and integrability : discrete spectral symmetries / S.P. Novikov -- Symmetries of spectral problems / A. Shabat -- Normal form and solitons / Y. Hirakoa and Y. Kodama -- Multiscale expansion and integrability of dispersive wave equations / A. Degasperis -- Painlevé tests, singularity structure and integrability / A.N.W. Hone -- Hirota's bilinear method and its connection with integrability / J. Hietarinta -- Integrability of the quantum XXZ Hamiltonian / T. Miwa.

Print version record.

This is a unique collection of lectures on integrability, intended forgraduate 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.