KdV & KAM / Thomas Kappeler, Jürgen Pöschel

This monograph is concerned with a natural question that arises once a partial differential equation – such as the Korteweg-de Vries (KdV) equation considered here – is understood as an infinite dimensional completely integrable Hamiltonian system. That question is whether the famous Kolmogorov-Arnold-Moser (KAM) Theorem for finite dimensional Hamiltonian systems can be extended to the infinite dimensional case. ... The book is extremely well written. It is intended to be self-contained and includes a number of appendices (in fact some eighty pages of appendices) which cover a variety of supporting topics, for example: Birkhoff normal forms, the spectra of Schrödinger operators on a finite interval, and symplectic geometry in infinite dimensions. In this way the book is made much more accesible than it might otherwise have been. The authors also intend that each chapter might be read independently; whilst they have certainly been successful in this, there remains the question of whether the resulting repetition is worth it or not. On balance it probably is, and in either case this is a minor quibble in an otherwise excellent text. ... (zbMath)