Differential Operators, Symmetries and the Inverse Problem for Second-Order Differential Equations
Articolo
Data di Pubblicazione:
1996
Citazione:
Differential Operators, Symmetries and
the Inverse Problem for Second-Order
Differential Equations / P. Morando, S. Pasquero. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - 3:1-2(1996), pp. 68-84. [10.2991/jnmp.1996.3.1-2.6]
Abstract:
With each second-order differential equation Z in the evolution space J1 (Mn+1) we associate, using the natural f(3,−1)-structure S and the f(3, 1)-structure K, a group G of automorphisms of the tangent bundle T(J1 (Mn+1))), with G isomorphic to a dihedral group of order 8. Using the elements of G and the Lie derivative, we introduce
new differential operators on J1 (Mn+1) and new types of symmetries of Z. We analyze the relations between the operators and the “dynamical” connection induced by Z. Moreover, we analyze the relations between the various symmetries, also in connection
with the inverse problem for Z. Both the approach based on the Poincarè–Cartan two forms and the one relying on the introduction of the so-called metrics compatible with Z are explicitly worked out.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Symmetry, Inverse Problem, Ordinary differential equations
Elenco autori:
P. Morando, S. Pasquero
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