Hamiltonian Systems of Hydrodynamic Type
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Authors
Reynolds, A. Patrick
Date
2010-12-23T20:54:41Z
Type
thesis
Language
eng
Keyword
Applied mathematics , Hydrodynamics , Hamiltonian systems , Differential geometry
Alternative Title
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
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This publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.