Related papers: A Direct Method for Obtaining the Differential Con…
The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether's…
The theory of special relativity can be generalized by means of a new principle called Conservation of Information. This allows a derivation of the constancy of the velocity of light with respect to moving frames, and, consequently, of…
Effective Field Theories with higher derivatives often yield equations of motion which define ill-posed problems. We present a method for enhancing control on such theories by coupling them to a field living in one extra dimension. The…
Lie-Poisson classical field theory is a field-theoretical model embedded in a non-commutative structure related to the framework of Poisson electrodynamics. In this paper, we follow the recently developed action principle for Lie-Poisson…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
The least action principle occupies a central part in contemporary physics. Yet, as far as classical field theory is concerned, it may not be as essential as generally thought. We show with three detailed examples of classical interacting…
We consider structure-preserving methods for conservative systems, which rigorously replicate the conservation property yielding better numerical solutions. There, corresponding to the skew-symmetry of the differential operator, that of…
An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is…
We introduce a methodology for seeking conservation laws within a Hamiltonian dynamical system, which we term ``neural deflation''. Inspired by deflation methods for steady states of dynamical systems, we propose to {iteratively} train a…
We lay down a set of requirements for a field theory to produce a covariant conservation law out of Noether's second theorem, and show that neither local invariance implies a covariant conservation law, nor the existence of a covariant…
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric…
Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to…
The derivation of conservation laws and invariant functions is an essential procedure for the investigation of nonlinear dynamical systems. In this study we consider a two-field cosmological model with scalar fields defined in the Jordan…
In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute…
We discuss the formulation of classical field theoretical models on $n$-dimensional noncommutative space-time defined by a generic associative star product. A simple procedure for deriving conservation laws is presented and applied to field…
We investigate conservation laws of diffusion-convection equations to construct first-order potential systems corresponding to these equations. We do two iterations of the construction procedure, looking, in the second step, for the…
A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…
The existing field theories are based on the properties of closed exterior forms, which are invariant ones and correspond to conservation laws for physical fields. Hence, to understand the foundations of field theories and their unity, one…
The existence of conservation laws is one of the most important requirement of physical theories. Some of them, like energy conservation, knows no experimental exception. However, the generalization of these conservation laws to curved…