# Verbovetsky A. Hamiltonian structures for general PDEs, talk at The Abel Symposium 2008, Differential Equations - Geometry, Symmetries and Integrability, 18-21 June 2008, Tromso, Norway (abstract)

**Speaker**: Alexander Verbovetsky

**Title**: Hamiltonian structures for general PDEs
**Abstract**:

We will discuss the following question: What happens to a Hamiltonian operator of an evolution system if we change coordinates so that the system becomes non-evolution?

We will give an answer to this question, describe the corresponding geometry, consider examples, in particular, construct a bihamiltonian structure for Kupershmidt's nonholonomic deformation of a bihamiltonian system.

**Slides**: Kersten P., Krasil'shchik I., Verbovetsky A., Vitolo R. Hamiltonian structures for general PDEs (presentation at The Abel Symposium 2008, Differential Equations - Geometry, Symmetries and Integrability, 18-21 June 2008, Tromso, Norway).pdf

**References**:

P. Kersten, I. Krasil'shchik, A. Verbovetsky, and R. Vitolo, *Hamiltonian structures for general PDEs*, Differential Equations - Geometry, Symmetries and Integrability: The Abel Symposium 2008 (B. Kruglikov, V. Lychagin, and E. Straume, eds.), Abel Symposia 5, Springer, 2009, pp. 187-198, arXiv:0812.4895