Nearly Integrable Infinite-Dimensional Hamiltonian Systems

1993
ISBN: 978-3-540-57161-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1556, 104 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 213 g

Reihe: Lecture Notes in Mathematics

The book is devoted to partial differential equations of
Hamiltonian form, close to integrable equations. For such
equations a KAM-like theorem is proved, stating that
solutions of the unperturbed equation that are quasiperiodic
in time mostly persist in the perturbed one. The theorem is
applied to classical nonlinear PDE's with one-dimensional
space variable such as the nonlinear string and nonlinear
Schr dinger equation andshow that the equations have
"regular" (=time-quasiperiodic and time-periodic) solutions
in rich supply.
These results cannot be obtained by other techniques. The
book will thus be of interest to mathematicians and
physicists working with nonlinear PDE's.
An extensivesummary of the results and of related topics is
provided in the Introduction. All the nontraditional
material used is discussed in the firstpart of the book and
in five appendices.

Zielgruppe

Research

Autoren/Hrsg.

Kuksin, Sergej B.

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Symplectic structures and hamiltonian systems in scales of hilbert spaces.- Statement of the main theorem and its consequences.- Proof of the main theorem.