Lecturer:
Course Type:
PhD Course
Academic Year:
2023-2024
Period:
March-April
Duration:
20 h
Description:
The course is centered on the Hamiltonian aspects of integrable systems of Ordinary and, especially, Partial Differential Equations, with a focus on the geometrical side.
Integrability will mean
Existence of a “sufficient number” of conservation laws.
Contents & schedule
- Symplectic and Poisson geometry: a reminder. Extensions to PDEs.
- The Marsden-Weinstein, Dirac and Marsden-Ratiu reduction schemes.
- Lie-Poisson structures on (duals of) Lie algebras. Drinfel’d-Sokolov reduction on loop algebras and equations of Korteweg - de Vries (KdV) - type
- Bihamiltonian structures and integrability.
- From the Hamiltonian structure of the Euler incompressible equations to the Hamiltonian structure of water-waves and, finally, to the bihamiltonian structure of the KdV equation.
Research Group:
Location:
TBC(to be checked)
Location:
A-005 (Wednesdays), 205 Main Building via Beirut (Fridays)