Sergej B. Kuksin – författare

This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.

The book is devoted to partial differential equations ofHamiltonian form, close to integrable equations. For suchequations a KAM-like theorem is proved, stating thatsolutions of the unperturbed equation that are quasiperiodicin time mostly persist in the perturbed one. The theorem isapplied to classical nonlinear PDE''s with one-dimensionalspace variable such as the nonlinear string and nonlinearSchr|dinger equation andshow that the equations have"regular" (=time-quasiperiodic and time-periodic) solutionsin rich supply.These results cannot be obtained by other techniques. Thebook will thus be of interest to mathematicians andphysicists working with nonlinear PDE''s.An extensivesummary of the results and of related topics isprovided in the Introduction. All the nontraditionalmaterial used is discussed in the firstpart of the book andin five appendices.