Related papers: Conservation laws for the Maxwell-Dirac equations …
We derive infinitely many conservation laws for some multi-dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear…
We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways.…
By the Cole-Hopf transformation, with any linear evolution equation in 1+1 dimensions a generalized Burgers equation is associated. We describe local conservation laws of these equations. It turns out that any generalized Burgers equation…
The macroscopic equations of Maxwell combined with a generalized form of the Lorentz law are a complete and consistent set; not only are these five equations fully compatible with the special theory of relativity, they also conform with the…
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.…
Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a…
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…
Structure-preserving algorithms for solving conservative PDEs with added linear dissipation are generalized to systems with time-dependent damping/driving terms. This study is motivated by several PDE models of physical phenomena, such as…
The two postulates of special relativity plus the postulates of conserved charges, both electric and magnetic, and a resulting linear system are sufficient for the derivation of the generalized vacuum Maxwell equations with both charges.…
We show that the laws of electromagnetism in $(D+1)$-dimensional Minkowski space-time $\mathcal{M}$, explicitly for $D=1$, $2$ and $3$, can be obtained from an integral representation of the zero-curvature equation in the corresponding loop…
It is shown that the Lorentz condition which is a conservation law on the electromagnetic four-vector-density A, plus the Lorentz transformation, taken together, are equivalent to the microscopic Maxwell's equations.
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical…
In this work we consider the problem on group classification and conservation laws of the general first order evolution equations. We obtain the subclasses of these general equations which are quasi-self-adjoint and self-adjoint. By using…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…
We derive a modified non-perturbative Lorentz-Abraham-Dirac equation. It satisfies the proper conservation laws, particularly, it conserves the generalized momentum, the latter property eliminates the symmetry-breaking runaway solution. The…
In 19th century Maxwell derived Maxwell equations from the knowledge of three experimental physical laws: the Coulomb's law, the Ampere's force law and Faraday's law of induction. However, theoretical basis for Ampere's force law and…
Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total…