Analysis of Hamiltonian Pdes

Erscheinungsjahr 2000
ISBN: 978-0-19-850395-8
Verlag: OUP Oxford

Buch, Englisch, 224 Seiten, laminated boards, Format (B × H): 161 mm x 240 mm, Gewicht: 511 g

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 will be an invaluable source of information for postgraduate mathematics and physics students and researchers.

Autoren/Hrsg.

Kuksin, Sergei B.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

- 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

Über Autor(innen)

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