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Please use this identifier to cite or link to this item: http://hdl.handle.net/1974/6254

Title: Hamiltonian Systems of Hydrodynamic Type

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Keywords: Applied mathematics
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 Graduate Theses and Dissertations
Department of Mathematics and Statistics Graduate Theses

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