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arXiv · 1402.4087

A new multisymplectic unified formalism for second-order classical field theories

Pedro D. Prieto-Martínez·Narciso Román-Roy
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Abstract

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincar\'e-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.

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Pedro D. Prieto-Martínez, Narciso Román-Roy. 2014-02-17. A new multisymplectic unified formalism for second-order classical field theories. https://doi.org/10.3934/jgm.2015.7.203

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