Muñoz Masqué, JaimePozo Coronado, Luis Miguel2023-06-202023-06-202005D. Bleecker: Gauge Theory and Variational Principles,Addison-Wesley Publishing Company, Inc., Reading,MA 1981. Th. Frankel: The Geometry of Physics, Cambridge University Press, Cambridge, UK 1997. H. Goldschmidt and S. Sternberg: The Hamilton-Cartan formalism in the Calculus of Variations, Ann. Inst.Fourier, Grenoble 23 (1973), 203-267. J. Grifone, J. Mufioz Masqu6 and L. M. Pozo Coronado:Variational first-order quasi-linear equations, L. Kozma, P. T. Nagy and L. Tamisy (Eds.), Proc. of the Colloquium on Differential Geometry, Steps in Differential Geometry, July 25-30, 2000, Debrecen (Hungary), Institute of Mathematics and Informatics, University of Debrecen, A. Hakovi and O. Krupkovai: Variational first-order partial differential equations, J. Diff. Equations 191 (2003), 67-89. S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, Volume I, Wiley, New York 1963. J. E. Marsden and S. Shkoller: Multisymplectic geometry, covariant Hamiltonians, and water waves, Math.Proc. Cambridge Philos. Soc. 125 (1999), no. 3, 553-575. J. Mufioz Masque and E. Rosado Maria: Invariant variational problems on linear frame bundles, Z Phys. A:Math. Gen. 35 (2002), 2013-2036. D. J. Saunders: The Geometry of Jet Bundles, Cambridge University Press, Cambridge, UK 1989. S. Sternberg: Lectures on Differential Geometry, Second edition, with an appendix by Sternberg and Victor W. Guillemin, Chelsea Publishing Co., New York 1983. J. J. Stawianowski: Field of linear frames as a fundamental self-interacting system, Rep. Math. Phys. 22 (1985), 323-371.0034-487710.1016/S0034-4877(05)80039-4https://hdl.handle.net/20.500.14352/50240The global inverse problem of the calculus of variations for the particular case of first-order quasi-linear PDEs is solved. Some examples in the field theory are discussed.engGlobal characterization of variational first-order quasi-linear equations.journal articlehttp://dx.doi.org/10.1016/S0034-4877(05)80039-4/science/article/pii/S0034487705800394http://dx.doi.org/10.1016/S0034-4877(05)80039-4restricted access512.7517.98Affine LagrangianEuler-Lagrange equationsFirst-order quasi-linear equationsJet bundlesPoincar6-Cartan form bundlesPoincar6-Cartan form.Geometria algebraicaAnálisis funcional y teoría de operadores1201.01 Geometría Algebraica