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Partial Differential Hamiltonian Systems

Published online by Cambridge University Press:  20 November 2018

Luca Vitagliano
DipMat, University of Salerno, and Istituto Nazionale di Fisica Nucleare, GC Salerno, via Ponte don Melillo, 84084 Fisciano (SA) Italy, e-mail:
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We define partial differential ( $\text{PD}$ in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, $\text{PD}$ Hamilton equations, $\text{PD}$ Noether theorem, $\text{PD}$ Poisson bracket, etc. Unlike the standard multisymplectic approach to Hamiltonian field theory, in our formalism, the geometric structure (kinematics) and the dynamical information on the “phase space” appear as just different components of one single geometric object.

Research Article
Copyright © Canadian Mathematical Society 2013


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