UID:
almahu_9947921574202882
Format:
XXVIII, 104 p.
,
online resource.
ISBN:
9783540479208
Series Statement:
Lecture Notes in Mathematics, 1556
Content:
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.
Note:
Symplectic structures and hamiltonian systems in scales of hilbert spaces -- Statement of the main theorem and its consequences -- Proof of the main theorem.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783540571612
Language:
English
Subjects:
Mathematics
URL:
http://dx.doi.org/10.1007/BFb0092243
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(Deutschlandweit zugänglich)
