Sergei B Kuksin

Analysis of Hamiltonian Pdes

• Gebundenes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Sydney University Press
• Seitenzahl: 224
• Erscheinungstermin: 9. November 2000
• Englisch
• Abmessung: 243mm x 162mm x 19mm
• Gewicht: 462g
• ISBN-13: 9780198503958
• ISBN-10: 0198503954
• Artikelnr.: 21565697

Autorenporträt

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

Inhaltsangabe

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