Nearly integrable infinite-dimensional Hamiltonian systems
著者
書誌事項
Nearly integrable infinite-dimensional Hamiltonian systems
（Lecture notes in mathematics, 1556）
Springer-Verlag, c1993
- : us
- : gw
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注記
Includes bibliographical references (p. 96-100) and index
内容説明・目次
内容説明
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.
目次
Symplectic structures and hamiltonian systems in scales of hilbert spaces.- Statement of the main theorem and its consequences.- Proof of the main theorem.
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