Integrability

• Corporate Author: SpringerLink (Online service)
• Other Authors: Mikhailov, Alexander V. (Editor)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Lecture Notes in Physics, 767
• Subjects: Physics.; Mathematical physics.; Mechanics.; Fluids.; Mathematical and Computational Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-88111-7

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...

Table of Contents:

• Introduction
• Symmetries of differential equations and the problem of Integrability
• Number theory and the symmetry classification of integrable systems
• Discretisation and Integrability. Discrete spectral symmetries
• Symmetries of spectral problems
• Normal forms and solitons
• Multiscale expansion and integrability of dispersive wave equations
• The Painlev ̌property and the poly-Painlev ̌test
• Hirota<U+0019>s bilinear method and its connection with integrability
• Integrability of the quantum XXZ Hamiltonian.