Abstract
Multi-symplectic formulations of Hamiltonian systems with two or more independent variables x α have been developed as a useful extension of Hamiltonian systems with one evolution variable t. This development has connections with dual variational formulations of traveling wave problems (e.g. Bridges (1992)), and is useful in numerical schemes for multisymplectic systems. Bridges and co-workers used the multi-symplectic approach to study linear and nonlinear wave propagation, generalizations of wave action, wave modulation theory, and wave stability problems (Bridges (1997a,b)). Reich (2000), and Bridges (2006) develop difference schemes. Multi-symplectic Hamiltonian systems have been studied by Marsden and Shkoller (1999) and Bridges et al. (2005). Bridges et al. (2010) shows the connection between multi-symplectic systems and the variational bi-complex.
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