Related papers: Conservation Laws of Variable Coefficient Diffusio…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
Viewing gravitational energy momentum $p_G^\mu$ as equal by observation, but different in essence from inertial energy-momentum $p_I^\mu$ requires two different symmetries to account for their independent conservations - spacetime and inner…
We formulate gauge invariance for the equilibrium statistical mechanics of classical multi-component systems. Species-resolved phase space shifting constitutes a gauge transformation which we analyze using Noether's theorem and shifting…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
We consider general, non-linear curvature perturbations on scales greater than the Hubble horizon scale by invoking an expansion in spatial gradients, the so-called gradient expansion. After reviewing the basic properties of the gradient…
In this paper, we are interested in a general equation that has finite speed of propagation compatible with Einstein's theory of special relativity. This equation without external force fields has been derived recently by means of optimal…
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Examples include Harry Dym equation,…
We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be utilized to solve the model. We show that for models where the conservation laws can be written in one-sided forms, like…
We find the group of equivalence transformations for equations of the form $y''= A(x)y' + F(y),$ where $A$ and $F$ are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method…
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena.…
This paper mainly contributes to the extension of Noether's theorem to differential-difference equations. For that purpose, we first investigate the prolongation formula for continuous symmetries, which makes a characteristic representation…
In our previous paper, the concept of sub-symmetry of a differential system was introduced, and its properties and some applications were studied. It was shown that sub-symmetries are important in decoupling a differential system, and in…
Within a strong coupling expansion, we construct local quasi-conserved operators for a class of Hamiltonians that includes both integrable and non-integrable models. We explicitly show that at the lowest orders of perturbation theory the…
The system of equations of one-dimensional shallow water over uneven bottom in Euler's and Lagrange's variables is considered. Intermediate system of equations is introduced. Hydrodynamic conservation laws of intermediate system of…
The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for *-invariant equations. The…
We investigate the relation between several generalized solution concepts for nonlinear PDE systems from fluid dynamics. More precisely, we study measure-valued solutions, dissipative weak solutions, and energy-variational solutions. For…
We propose a notion of hyperbolic system of conservation laws invariant for the Galileo group of transformations. We show that with natural physical and mathematical hypotheses, such a system conducts to the gas dynamics equations or to…
A complete classification of all low-order conservation laws is carried out for a system of coupled semilinear wave equations which is a natural two-component generalization of the nonlinear Klein-Gordon equation. The conserved quantities…
We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation…
In this paper we introduce, inspired by Clausius and developing the ideas of \cite{pre}, the concept of equivalence of transformations in non equilibrium theory of diffusive systems within the framework of macroscopic fluctuation theory.…