Symmetries of the Generalized Variational Functional of Herglotz for Several Independent Variables

Abstract

This paper provides a method for calculating the symmetry groups of the functional defined by the generalized variational principle of Herglotz in the case of several independent variables. Examples of calculating variational symmetry groups are given, including those for the non-conservative nonlinear Klein-Gordon equation, and for the equations describing the propagation of electromagnetic fields in a conductive medium.