Related papers: Conservation laws for self-adjoint first order evo…
We present a new derivation of the equations governing the oscillations of slowly rotating relativistic stars. Previous investigations have been mostly carried out in the Regge-Wheeler gauge. However, in this gauge the process of…
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…
In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural…
The Einstein equations have proven surprisingly difficult to solve numerically. A standard diagnostic of the problems which plague the field is the failure of computational schemes to satisfy the constraints, which are known to be…
This paper gives a general treatment and proof of the direct conservation law method presented in Part I. In particular, the treatment here applies to finding the local conservation laws of any system of one or more partial differential…
We consider two discrete completely integrable evolutions: the Toda Lattice and the Ablowitz-Ladik system. The principal thrust of the paper is the development of microscopic conservation laws that witness the conservation of the…
For $2\X2$ systems of conservation laws satisfying Bakhvalov conditions, we present a class of damping terms that still yield the existence of global solutions with periodic initial data of possibly large bounded total variation per period.…
We study the nonlinear wave equation for arbitrary function with fourth order dissipation. A special case that is analysed exclusively is the model of nerve membranes; we consider this model, both, in the presence and absence of the fourth…
In the present paper we consider nonlinear multidimensional Cahn-Hilliard and Kuramoto-Sivashinsky equations that have many important applications in physics and chemistry, and a certain natural generalization of these equations. For an…
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation…
A geometrical formulation for adjoint-symmetries as 1-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution…
We analyse the conservative evolution of spinning compact binaries to second post-Newtonian (2PN) order accuracy, with leading order spin-orbit, spin-spin and mass quadrupole-monopole contributions included. As a main result we derive a…
We study the lowest order conservation laws in one-dimensional (1D) integrable quantum many-body models (IQM) as the Heisenberg spin 1/2 chain, the Hubbard and t-J model. We show that the energy current is closely related to the first…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
In this paper, we construct and analyse the symmetries and conservation laws (conserved densities) of a model of a nonlinear Scrodinger equation with PT-symmetric potentials and inhomogeneity.
We classify zeroth-order conservation laws of systems from the class of two-dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The classification is carried out…
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially…
Preliminary group classification for a class of generalized inviscid Burger's equations in the general form $u_t+g(x, u)u_x = f(x, u)$ is given and additional equivalence transformations are found. Adduced results complete and essentially…
We derive a fundamental conservation law of operator current for master equations describing reduced quantum systems. If this law is broken, the temporal integral of the current operator of an arbitrary system observable does not yield in…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…