Partial Differential Hamiltonian Systems

Abstract

We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in 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.

30 pages, the current version agrees with the published version

References in corpus (6)

• The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories
• Multisymplectic formulation of fluid dynamics using the inverse map
• Secondary Calculus and the Covariant Phase Space
• The Tulczyjew triple for classical fields
• Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories
• On similarity classes of well-rounded sublattices of ${\mathbb{Z}}^2$

Cited by in corpus (7)

• The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories
• Hamilton-Jacobi Diffieties
• Tulczyjew triples: from statics to field theory
• Multisymplectic formalism and the covariant phase
• Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings
• On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective
• Variational Principles for multisymplectic second-order classical field theories