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Title: Nearly Integrable Infinite-Dimensional Hamiltonian Systems ([EBook]) / by Sergej B. Kuksin. Dewey Class: 515 Author: Kuksin, Sergej Borisovich, 1955- Publication: Berlin, Heidelberg : Springer, 1993. Other name(s): SpringerLink (Online service) Physical Details: XXVIII, 104 pages : online resource. Series: Lecture Notes in Mathematics,0075-8434 ;; 1556 ISBN: 9783540479208 System details note: Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) Summary Note: 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.: Contents note: Symplectic structures and hamiltonian systems in scales of hilbert spaces -- Statement of the main theorem and its consequences -- Proof of the main theorem. ------------------------------ *** There are no holdings for this record *** -----------------------------------------------
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