148432 20260225150302.0 doi 10.1063/1.5004260 sideral 101980 ART-2017-101980 eng Léon, M. de Hamilton-jacobi theory in multisymplectic classical field theories 2017 Access copy available to the general public Unrestricted The geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de Léon et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results. info:eu-repo/grantAgreement/ES/AGAUR/2009 SGR1338 info:eu-repo/grantAgreement/ES/DGA/E24-1 info:eu-repo/grantAgreement/EC/FP7/246981/EU/Geometric Mechanics/GEOMECH info:eu-repo/grantAgreement/ES/MICINN/MTM2011-15725-E info:eu-repo/grantAgreement/ES/MICINN/MTM2011-22585 info:eu-repo/grantAgreement/ES/MINECO/MTM2013-42870-P info:eu-repo/grantAgreement/ES/MINECO/SEV-2011-0087 info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.165 2017 PHYSICS, MATHEMATICAL 31 / 55 = 0.564 2017 Q3 T2 0.644 2017 Mathematical Physics 2017 Q2 Statistical and Nonlinear Physics 2017 Q3 info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion Prieto-Martinez, P. D. Roman-Roy, N. Vilariño, S. (orcid)0000-0003-0404-1427 58, 9 (2017), 092901 [44 pp] J. math. phys. JOURNAL OF MATHEMATICAL PHYSICS 0022-2488 654988 http://zaguan.unizar.es/record/148432/files/texto_completo.pdf Preprint 1601877 http://zaguan.unizar.es/record/148432/files/texto_completo.jpg?subformat=icon icon Preprint oai:zaguan.unizar.es:148432 articulos driver 2026-02-25-14:59:50 ARTICLE