Related papers: A Direct Method for Obtaining the Differential Con…
In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the…
We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first order Lagrangian by boundary terms only. A new method of deriving…
In a previous work we showed that, in a suitable setting, one can use diffeomorphism invariance in order to derive gravitational field equations from boundary terms of the gravitational action. Standing by our results we reply here to a…
It is known that action is invariant in special relativity. The goal of this note is to show that the reverse statement is also correct, that special relativity follows from the postulate that action is invariant under the transformation…
We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the…
In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we…
We present a unified theory to treat conservation laws in light-matter interactions. It can be used to describe and engineer the transfer of any measurable property from the electromagnetic field to any object. The theory allows to…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
The direct method of construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems [Anco S. and Bluman G., Direct construction method for conservation laws…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a…
A role of the exterior differential forms in field theory is connected with a fact that they reflect properties of the conservation laws. In field theory a role of the closed exterior forms is well known. A condition of closure of the form…
The purpose of this article is to extend the applicability of the stationarity principle of the full Jacobi action to non-conservative natural systems and to derive equations of motion corresponding to this extended principle. To this end,…
We investigate the possible form of local translation invariant conservation laws associated with the relativistic field equations $\partial\bar\partial\phi_i=-v_i(\bphi)$ for a multicomponent field $\bphi$. Under the assumptions that…
In this paper a mathematically precise global (i.e. not the usual local) approach is presented to the variational principles of general relativistic classical field theories. Problems of the classic (usual) approaches are also discussed in…