Variational principles for differential equations with symmetries and conservation laws. II. Polynomial differential equations.
Ian M. Anderson, Juha Pohjanpelto (1995)
Mathematische Annalen
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Ian M. Anderson, Juha Pohjanpelto (1995)
Mathematische Annalen
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Jana Musilová, Stanislav Hronek (2016)
Communications in Mathematics
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As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples...
Marcella Palese (2016)
Communications in Mathematics
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We will pose the inverse problem question within the Krupka variational sequence framework. In particular, the interplay of inverse problems with symmetry and invariance properties will be exploited considering that the cohomology class of the variational Lie derivative of an equivalence class of forms, closed in the variational sequence, is trivial. We will focalize on the case of symmetries of globally defined field equations which are only locally variational and prove that variations...
Śladkowska, Janina (2015-11-13T13:54:55Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Gerhard Ströhmer (1985)
Mathematische Annalen
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W. M. Mikulski (2009)
Annales Polonici Mathematici
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We prove that the most interesting operators in the Euler-Lagrange complex from the variational bicomplex in infinite order jet spaces are determined up to multiplicative constant by the naturality requirement, provided the fibres of fibred manifolds have sufficiently large dimension. This result clarifies several important phenomena of the variational calculus on fibred manifolds.
Marcella Palese, Ekkehart Winterroth, E. Garrone (2011)
Archivum Mathematicum
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We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we...
Krupka, D. (2006)
Lobachevskii Journal of Mathematics
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Gerhard Ströhmer (1984)
Mathematische Zeitschrift
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Jean Ollagnier, Didier Pinchon (1982)
Studia Mathematica
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Veronika Chrastinová, Václav Tryhuk (2018)
Mathematica Bohemica
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Some open problems appearing in the primary article on the symmetry reduction are solved. A new and quite simple coordinate-free definition of Poincaré-Cartan forms and the substance of divergence symmetries (quasisymmetries) are clarified. The unbeliavable uniqueness and therefore the global existence of Poincaré-Cartan forms without any uncertain multipliers for the Lagrange variational problems are worth extra mentioning.
Zhang, Weimin (2009)
Mathematical Problems in Engineering
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