Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.506178
Title: Classification of integrable hydrodynamic chains using the Haantjes tensor
Author: Marshall, David G.
Awarding Body: Loughborough University
Current Institution: Loughborough University
Date of Award: 2008
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Abstract:
The integrability of an m-component system of hydrodynamic type, Ut = v(u)ux, by the generalized hodograph method requires the diagonalizability of the m x m matrix v(u). The diagonalizability is known to be equivalent to the vanishing of the corresponding Haantjes tensor. This idea is applied to hydrodynamic chains - infinite-component systems of hydrodynamic type for which the 00 x 00 matrix v(u) is 'sufficiently sparse'. For such 'sparse' systems the Haantjes tensor is well-defined, and the calculation of its components involves only a finite number of summations. The calculation of the Haantjes tensor is done by using Mathematica to perform symbolic calculations. Certain conservative and Hamiltonian hydrodynamic chains are classified by setting Haantjes tensor equal to zero and solving the resulting system of equations. It is shown that the vanishing of the Haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi-Hamiltonian hydrodynamic reductions, thus providing an easy-to-verify necessary condition for the integrability of such sysyems. In the cases of the Hamiltonian hydrodynamic chains we were able to first construct one extra conservation law and later a generating function for conservation laws, thus establishing the integrability.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.506178  DOI: Not available
Keywords: Integrability ; Nijenhuis tensor ; Haantjes tensor ; Hydrodynamic chains ; Benney chain ; Diagonalizability ; Generating function of conservations laws
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