Nearly Integrable Infinite-Dimensional Hamiltonian Systems
Title | Nearly Integrable Infinite-Dimensional Hamiltonian Systems PDF eBook |
Author | Sergej B. Kuksin |
Publisher | Springer |
Pages | 128 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540479201 |
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.
Quasiperiodic Solutions of Nearly Integrable Infinite-dimensional Hamiltonian Systems
Title | Quasiperiodic Solutions of Nearly Integrable Infinite-dimensional Hamiltonian Systems PDF eBook |
Author | Sergei B. Kuksin |
Publisher | |
Pages | 111 |
Release | 1991 |
Genre | |
ISBN |
Quasiperiodic solutions of nearly integrable infinite-dimensional Hamiltonian systems
Title | Quasiperiodic solutions of nearly integrable infinite-dimensional Hamiltonian systems PDF eBook |
Author | S. B. Kuksin |
Publisher | |
Pages | 107 |
Release | 1991 |
Genre | |
ISBN |
Properties of Infinite Dimensional Hamiltonian Systems
Title | Properties of Infinite Dimensional Hamiltonian Systems PDF eBook |
Author | P.R. Chernoff |
Publisher | Springer |
Pages | 165 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540372873 |
Infinite Dimensional Hamiltonian Systems
Title | Infinite Dimensional Hamiltonian Systems PDF eBook |
Author | Rudolf Schmid |
Publisher | |
Pages | 178 |
Release | 1987 |
Genre | Science |
ISBN |
Lectures on Integrable Systems
Title | Lectures on Integrable Systems PDF eBook |
Author | Jens Hoppe |
Publisher | Springer Science & Business Media |
Pages | 109 |
Release | 2008-09-15 |
Genre | Science |
ISBN | 3540472746 |
Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.
Properties of Infinite Dimensional Hamiltonian Systems
Title | Properties of Infinite Dimensional Hamiltonian Systems PDF eBook |
Author | Paul R. Chernoff |
Publisher | |
Pages | 160 |
Release | 1974 |
Genre | Dynamics |
ISBN |