In the present Thesis, we deal mainly with the subclass of Hamiltonian evolutionary PDEs and their Poisson brackets (PBs). We address the problem of classifying discrete differential-geometric PBs (dDGPBs) of any fixed order on target space of dimension 1 and describing their compatible pencils. Furthermore, we explain a new criterium about the existence of tri-Hamiltonian structures for nonlinear wave systems.

Classification problems for Hamiltonian evolutionary equations and their discretizations / Parodi, Emanuele. - (2012 Oct 25).

Classification problems for Hamiltonian evolutionary equations and their discretizations

Parodi, Emanuele
2012-10-25

Abstract

In the present Thesis, we deal mainly with the subclass of Hamiltonian evolutionary PDEs and their Poisson brackets (PBs). We address the problem of classifying discrete differential-geometric PBs (dDGPBs) of any fixed order on target space of dimension 1 and describing their compatible pencils. Furthermore, we explain a new criterium about the existence of tri-Hamiltonian structures for nonlinear wave systems.
Dubrovin, Boris
Parodi, Emanuele
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/4704
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