Georgieva, B. and Guenther, R.B. (2002) First Noether-Type Theorem for the Generalized Variational Principle of Herglotz. Topological Methods in Nonlinear Analysis, 20, 261-273.
https://doi.org/10.12775/tmna.2002.036

has been cited by the following article:

• TITLE: Evolutionary Nonconservative Field Theories

  AUTHORS: Bogdana A. Georgieva

  KEYWORDS: Mathematical Methods in Quantum Theory, Nonconservative Quantum Systems, Nonconservative Systems, Exact Methods for Solution of Pdes, Nonconservative Systems, Integrable Nonconservative Systems, Nonconservative Systems of Variational Origin, Nonconservative Processes

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.3, March 19, 2025

  ABSTRACT: This paper introduces a new evolutionary system which is uniquely suitable for the description of nonconservative systems in field theories, including quantum mechanics, but is not limited to it only. This paper also introduces a new exact method of solution for such nonconservative systems. These are significant contributions because the vast majority of nonconservative systems with several independent variables do not have self-adjoint Frechet derivatives and because of that can not benefit from the exact methods of the classical calculus of variations. The new evolutionary system is rigorously mathematically derived and the new method for solution is mathematically proved to be applicable to systems of PDEs of second order for nonconservative process. As examples of applications, the method is applied to several nonconservative systems: the propagation of electromagnetic fields in a conductive medium, the nonlinear Schrodinger equation with electromagnetic interactions, and others.