576 citations · 1.9k across the 50 of their papers we have counts for
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Multisymplectic geometry, covariant Hamiltonians, and water waves
Jerrold E. Marsden, Steve Shkoller
This paper concerns the development and application of the multisymplectic Lagrangian and Hamiltonian formalism for nonlinear partial differential equations. In this theory, soluti…
Multisymplectic geometry, variational integrators, and nonlinear PDEs
Jerrold E. Marsden, George W. Patrick, Steve Shkoller
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fund…
The Maxwell-Vlasov equations in Euler-Poincare form
H. Cendra, D. D. Holm, M. J. W. Hoyle +1
Low's well known action principle for the Maxwell-Vlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables. By…
The Euler-Poincare Equations and Semidirect Products with Applications to Continuum Theories
D. D. Holm, J. E. Marsden, T. S. Ratiu
We study Euler-Poincare systems (i.e., the Lagrangian analogue of Lie-Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Eul…
Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory
Mark J. Gotay, James Isenberg, Jerrold E. Marsden +1
This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of…