Related papers: Conservation laws in Skyrme-type models
We consider $f\left(R\right) $-gravity in a Friedmann-Lema\^itre-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of $f\left(R\right) $ and…
We give a full analysis of the conservation along null surfaces of generalized energy and super-momenta, for gravitational systems enclosed by a finite boundary. In particular we interpret the conservation equations in a canonical manner,…
We provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. We find that the conserved current and the associated conserved charge…
There is a well-known short list of asymptotic conserved quantities for a physical system at spatial infinity. We search for new ones.This is carried outwithin the asymptotic framework of Ashtekar and Romano, in which spatial infinity is…
A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound…
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…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
An essentially complete new paradigm for dynamical black holes in terms of trapping horizons is presented, including dynamical versions of the physical quantities and laws which were considered important in the classical paradigm for black…
The construction of fractional derivatives with the right properties for use in field theory is reputed to be a difficult task, essentially because of the absence of a unique definition and uniform properties. The conformable fractional…
Being gauge non-invariant, a Chern-Simons (2k-1)-form seen as a Lagrangian of gauge theory on a (2k-1)-dimensional manifold leads to the gauge conservation law of a modified Noether current.
It is known that corresponding to each isometry there exist a conserved quantity. It is also known that the Lagrangian of the line element of a space is conserved. Here we investigate the possibility of the existence of "new" conserved…
In the present article we show that the Skyrme--Faddeev model possesses nonlinear wave solutions, which can be expressed in terms of elliptic functions. The Whitham averaging method has been exploited in order to describe slow deformation…
We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
A general scalar-tensor theory of gravity carries a conserved current for a trace free minimally coupled scalar field, under the condition that the potential $V(\phi)$ of the nonminimally coupled scalar field is proportional to the square…
The concept of quasi-integrability has been examined in the context of deformations of the defocusing non-linear Schr\"odinger model (NLS). Our results show that the quasi-integrability concept, recently discussed in the context of…
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…
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…
In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many…
This lecture provides a pedagogical instruction to the basic concepts of the Skyrme model and its some applications. As the preliminary for understanding the Skyrme model, we first briefly explain the large $N_c$ expansion, chiral symmetry…