For the last 20-30 years, interest among mathematicians and physicists in infinite-dimensional Hamiltonian systems and Hamiltonian partial differential equations has been growing strongly, and many papers and a number of books have been written on integrable Hamiltonian PDEs. During the last decade though, the interest has shifted steadily towards non-integrable Hamiltonian PDEs. Here, not algebra but analysis and symplectic geometry are the appropriate analysing tools. The present book is the first one to use this approach to Hamiltonian PDEs and present a complete proof of the "KAM for PDEs" theorem. It will be an invaluable source of information for postgraduate mathematics and physics students and researchers.
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Sergei B. Kuksin, Professor of Mathematics, Heriot-Watt University, Edinburgh, and Steklov Mathematical Institute, MoscowReview:
"The aim of this book is to present the following form of the proof of Kolmogorov-Arnold-Moser (KAM) theorem: most of the space-periodic finite-gap solutions of a Lax-integrable Hamiltonian partial differential equations (PDE) persist under a small perturbation of the equation as timequasiperiodic solutions of the perturbed equation. This theorem provides an important tool for an effective study of PDEs."--EMS
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