From PDE Systems and Metrics to Generalized Field Theories

Abstract

The paper proved that every $C^2$-solution of a given first order PDEs system, regarded on the jet fibre bundle of order one $J^1(T,M)$, may be viewed as a "generalized harmonic map", via the least squares variational method. Our ideas are structured in the following way: 1) we find a suitable geometrical structure on $J^1(T,M)$ that convert the solutions of the given PDEs system into "generalized harmonic maps"; 2) we build a natural geometry induced by a such PDEs system; 3) we construct a field theory, in a general setting, naturally attached to this PDEs system.

The authors express their sincere thanks to Professors V. Balan, V. Obadeanu and D. Opris for their critical reading of an earlier version of this paper

References in corpus (1)

• The Geometry of Autonomous Metrical Multi-Time Lagrange Space of Electrodynamics

Cited by in corpus (4)

• Periodical Solutions of Multi-Time Hamilton Equations
• Some Inequalities Satisfied by Periodical Solutions of Multi-Time Hamilton Equations
• Poisson-Gradient Dynamical Systems with Convex Potential
• Poisson-Gradient Dynamical Systems with Bounded Non-Linearity