Analysis of Hamiltonian PDEs [Hardcover]

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.

Preface
Notations
I. Unperturbed equations
1. Some analysis in Hilbert spaces and scales
2. Integrable subsystems and Lax-integrable equations
3. Finite-gap manifolds for the KdV equation and theta-formulas
4. Sine-Gordon equation
5. Linearised equations and their Floquet solutions
6. Linearised Lax-integrable equations
7. Normal forms
II. Perturbed equations
1. A KAM theorem for perturbed nonlinear equations
2. Examples
3. Proof of KAM-theorem on parameter-depending equations
4. Linearised equations
5. First-order linear differential equations on n-torus
Addendum: The theorem of A.N. Kolmogorov
Index
Bibliography

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

The book was written to present a complete proof of the following infinite-dimensional KAM theorem: most space-periolc*