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A new multisymplectic unified formalism for second order classical field theories

2015; American Institute of Mathematical Sciences; Volume: 7; Issue: 2 Linguagem: Inglês

10.3934/jgm.2015.7.203

1941-4897

Pedro Daniel Prieto-Martínez, Narciso Román‐Roy,

Numerical methods for differential equations

We present a new multisymplectic framework for second-order classical field theories which is basedon an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. Thismodel provides a straightforward and simple way to define the Poincaré-Cartan form and clarifiesthe construction of the Legendre map (univocally obtained as a consequence of the constraintalgorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the fieldequations, which are analyzed in-depth, and written in terms of holonomic sections and multivectorfields. Our treatment therefore completes previous attempt to achieve this aim. The formulation isapplied to describing some physical examples; in particular, to giving another alternativemultisymplectic description of the Korteweg-de Vries equation.