|
QSpace at Queen's University >
Theses, Dissertations & Graduate Projects >
Queen's Theses & Dissertations >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/1974/6254
|
| Title: | Hamiltonian Systems of Hydrodynamic Type |
| Authors: | REYNOLDS, A PATRICK |
|
|
| Keywords: | Applied mathematics
Hydrodynamics
Hamiltonian systems
Differential geometry |
| Issue Date: | 2010 |
| Series/Report no.: | Canadian theses |
| Abstract: | We study the Hamiltonian structure of an important class of nonlinear partial differential equations: the so-called systems of hydrodynamic type, which are first-order in tempo-spatial variables, and quasi-linear. Chapters 1 and 2 constitute a review of background material, while Chapters 3, 4, 5 contain new results, with additional review sections as necessary. In Chapter 3 we demonstrate, via the Nijenhuis tensor, the integrability of a system of hydrodynamic type derived from the classical Volterra system. In Chapter 4, families of Hamiltonian structures of hydrodynamic type are constructed, as well as a gauge transform acting on Hamiltonian structures of hydrodynamic type. In Chapter 5, we present necessary and sufficient criteria for a three-component system of hydrodynamic type to be Hamiltonian, and classify the Lie-algebraic structures induced by a Hamiltonian structure for four-component systems of hydrodynamic type. |
| Description: | Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2010-12-23 11:35:41.976 |
| URI: | http://hdl.handle.net/1974/6254 |
| Appears in Collections: | Queen's Theses & Dissertations
Mathematics & Statistics Graduate Theses
|
Items in QSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
|
