Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2000-02-08
Nonlinear Sciences
Exactly Solvable and Integrable Systems
55 pages, Latex with amsmath and amssymb. Lectures given by F. Magri at the 1999 CIME course ``Direct and Inverse Methods in S
Scientific paper
The aim of these lectures is to show that the methods of classical Hamiltonian mechanics can be profitably used to solve certain classes of nonlinear partial differential equations. The prototype of these equations is the well-known Korteweg-de Vries (KdV) equation. In these lectures we touch the following subjects: i) The birth and the role of the method of Poisson pairs inside the theory of the KdV equation; ii) the theoretical basis of the method of Poisson pairs; iii) the Gel'fand-Zakharevich theory of integrable systems on bihamiltonian manifolds; iv) the Hamiltonian interpretation of the Sato picture of the KdV flows and of its linearization on an infinite-dimensional Grassmannian manifold. v)the reduction technique and its use to construct classes of solutions; iv) the role of the technique of separation of variables in the study of the reduced systems. vii) some relations intertwining the method of Poisson pairs with the method of Lax pairs.
Falqui Gregorio
Magri Franco
Pedroni Marco
No associations
LandOfFree
The method of Poisson pairs in the theory of nonlinear PDEs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The method of Poisson pairs in the theory of nonlinear PDEs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The method of Poisson pairs in the theory of nonlinear PDEs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-558524