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A note on Hamiltonian structure

Published online by Cambridge University Press:  24 October 2008

S. Bowman
S. Bowman
Affiliation:
Department of Mathematics, University of Chicago, Chicago, IL 60637, U.S.A.
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Extract

The aim of this paper is to give some results on the determination of Hamiltonian structure for a set of evolutionary equations, either differential or non-local. There are several reasons why the recognition of Hamiltonian structure is important. Firstly, as in the case of Lagrangian systems, conservation laws are often connected with symmetry groups of the equations. This point is addressed in §4. Secondly, variational principles for steady solutions can often be found by restricting attention to the steady equations. Connected to the second point, methods have been developed by Arnol'd[2] and more recently by Marsden, Weinstein etc. (see, e.g. [24]) to study the nonlinear stability of steady solutions, on lines similar to the proof of nonlinear stability for the solitary-wave solution of the Korteweg–de Vries equation by Benjamin [4] and Bona[9].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 102 , Issue 1 , July 1987 , pp. 173 - 189
Copyright
Copyright © Cambridge Philosophical Society 1987

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References

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