A new multisymplectic unified formalism for second order classical field theories
PublisherAmerican Institute of Mathematical Sciences
Rights accessOpen Access
We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified LagrangianHamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincare-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.
CitationP.D. Prieto-Martínez, Roman-Roy, N. A new multisymplectic unified formalism for second order classical field theories. "Journal of Geometric Mechanics", 01 Juny 2015, vol. 7, núm. 2, p. 203-253.