Here is a partial list, that I plan to gradually add to, of very good
textbooks on integrable models. Only self-contained textbook style
texts will be included.
Introduction to Classical Integrable Systems
by O Babelon, D Bernard and M Talon, is the most comprehensive introduction
to classical integrable models. It covers basically all approaches to
the theory, and more importantly discusses the relationships between
them. The authors try very hard to make the book self contained, but
the breadth of the material covered makes it at times rather advanced
reading.
The Direct Method in Soliton Theory
by R Hirota is an elementary introduction to Sato's theory.
It contains explicit caculations with emphasis on the Toda
lattice. The book doesn't go as deeply into the theory as
Solitons by Miwa, Jimbo and Date.
Soliton Equations and Hamiltonian Systems
by L A Dickey is a very well written, very comprehensive introduction
to classical integrable models. Contains topics and models that I haven't
seen discussed in any detail anywhere else.
Solitons, Nonlinear Evolution Equations and Inverse Scattering
by M A Ablowitz and P A Clarkson, is a comprehensive introduction
to the inverse scattering transform. It also includes an introduction
to the Painleve equations.
Integrability: The Seiberg-Witten and Witham Equations
edited by H W Braden and I M Krichever, is a collection of (mostly)
introductory papers on applications of classical integrable models
in modern mathematical physics of the string theory type. Highly
recommended to get an overview of this research.
Back to homepage