Analysis of Hamiltonian PDEs

Hardcover | September 15, 2000

bySergei B. Kuksin

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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 lastdecade 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 will be an invaluable source ofinformation for postgraduate mathematics and physics students and researchers.

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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 lastdecade though, the interest has shifted stead...

Sergei B. Kuksin, Professor of Mathematics, Heriot-Watt University, Edinburgh, and Steklov Mathematical Institute, Moscow

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Format:HardcoverPublished:September 15, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198503954

ISBN - 13:9780198503958

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Table of Contents

PrefaceNotationsI. Unperturbed equations1. Some analysis in Hilbert spaces and scales2. Integrable subsystems and Lax-integrable equations3. Finite-gap manifolds for the KdV equation and theta-formulas4. Sine-Gordon equation5. Linearised equations and their Floquet solutions6. Linearised Lax-integrable equations7. Normal formsII. Perturbed equations1. A KAM theorem for perturbed nonlinear equations2. Examples3. Proof of KAM-theorem on parameter-depending equations4. Linearised equations5. First-order linear differential equations on n-torusAddendum: The theorem of A.N. KolmogorovIndexBibliography