Nearly integrable infinite-dimensional Hamiltonian systems
Author(s)
Bibliographic Information
Nearly integrable infinite-dimensional Hamiltonian systems
（Lecture notes in mathematics, 1556）
Springer-Verlag, c1993
- : us
- : gw
Available at 89 libraries
Note
Includes bibliographical references (p. 96-100) and index
Description and Table of Contents
Description
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.
Table of Contents
Symplectic structures and hamiltonian systems in scales of hilbert spaces.- Statement of the main theorem and its consequences.- Proof of the main theorem.
by "Nielsen BookData"