Multi-Hamiltonian structure of equations of hydrodynamic type

Date
1990
Authors
Gümral, H.
Nutku, Y.
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Source Title
Journal of Mathematical Physics
Print ISSN
0022-2488
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Publisher
A I P Publishing LLC
Volume
31
Issue
11
Pages
2606 - 2611
Language
English
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Abstract

We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation governing the motion of plane sound waves of nite amplitude and another quasi-linear second order wave equation. There exists a doubly in- nite family of conserved Hamiltonians for the equations of gas dynamics which degenerate into one, namely the Benney sequence, for shallow water waves. We present further in nite sequences of conserved quantities for these equations. In the case of multi-component equations of hydrodynamic type, we show that Kodama's generalization of the shallow water equations admits bi-Hamiltonian structure.

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Published Version (Please cite this version)