Nearly integrable infinite-dimensional Hamiltonian systems / Sergej B. Kuksin.Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1556.Publication details: Berlin ; New York : Springer-Verlag, ©1993. Description: 1 online resource (xxvii, 101 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540479208; 3540479201Subject(s): Hamiltonian systems | Schrödinger equation | Systèmes hamiltoniens | Équation de Schrödinger | Hamiltonian systems | Schrödinger equation | Globale analyse | Integrables System | Hamiltonsches System | Unendlichdimensionales System | Systèmes hamiltoniens | Schrödinger, Équation deGenre/Form: Electronic books. Additional physical formats: Print version:: Nearly integrable infinite-dimensional Hamiltonian systems.DDC classification: 515.39 LOC classification: QA614.83 | .K85 1993QA3 | .L28 no. 1556Other classification: 31.55 Online resources: Click here to access online
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Includes bibliographical references (pages 96-100) and index.
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.
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Symplectic structures and hamiltonian systems in scales of hilbert spaces -- Statement of the main theorem and its consequences -- Proof of the main theorem.