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Quasilinear Hamiltonian systems

Published online by Cambridge University Press:  14 November 2011

Jan S. Rogulski
Jan S. Rogulski
Affiliation:
Institute of Mathematics, Warsaw Technical University, Pl. Jedności Robotniczej 1, 00-661 Warszawa, Poland
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Synopsis

We consider quasilinear systems of 2N partial differential equations with 2N unknown functions depending on n + 1 variables as evolution systems on the space L2(Rn, RN) × L2(Rns, RN) endowed with a symplectic form induced by the standard scalar product on L2(Rn, RN). The necessary and sufficient conditions for such a system to be a Hamiltonian system are derived. The main purpose of this paper is to propose a straightforward link between the symplectic approach formulated by Chernoff, Hughes and Marsden and the multisymplectic formulations of evolution systems created by Kijowski and developed by Gawedzki and Kondracki. A general method of constructing the multisymplectic form and the Hamiltonian form for these systems is given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 195 - 204
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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