Related papers: Conservation laws in Skyrme-type models
The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on…
A four dimensional conformally invariant energy is studied. This energy generalises the well known two-dimensional Willmore energy. Although not positive definite, it includes minimal hypersurfaces as critical points. We compute its first…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
A generalization of implicit conservative numerics to multiple dimensions requires advanced concepts of tensor analysis and differential geometry and hence a more thorough dedication to mathematical fundamentals than maybe expected at first…
In the semi-classical approach to the Skyrme model, nuclei are approximated by quantum mechanical states on a finite-dimensional space of field configurations; in zero-mode quantization this space is generated by rotations and isorotations.…
In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as…
Zero-range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond- mean-field models, an artificial ultraviolet divergence is generated by the…
Extensivity of conservation laws of the quantum Hirota model on a $1+1$ dimensional lattice is considered. This model can be interpreted in terms of an integrable many-body quantum Floquet dynamics. We establish the procedure to generate a…
We propose a generalization of the False Vacuum Skyrme model for any simple compact Lie groups $G$ that leads to Hermitian symmetric spaces. The Skyrme field that in the original theory takes its values in $SU(2)$ Lie group, now takes its…
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a…
This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…
Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics.…
Conservation of current and conservation of charge are nearly the same thing: when enough is known about charge movement, conservation of current can be derived from conservation of charge, in ideal dielectrics, for example. Conservation of…
Every spacetime that is asymptotically flat near null infinity can be conformally mapped via a spatial inversion onto the geometry around an extremal, non-rotating and non-expanding horizon. We set up a dictionary for this geometric…
The concept of nonlinear self-adjointness is employed to construct the conservation laws for fractional evolution equations using its Lie point symmetries. The approach is demonstrated on subdiffusion and diffusion-wave equations with the…
We study the noncommutative extensions of certain integrable field theories, namely the sine- and sinh-Gordon (sG and shG) models, and the U(N) principal chiral model (pcm). We argue that the Moyal deformations of the sG and shG models are…
We consider a class of scale-invariant curvature energies defined on immersed $4$-dimensional manifolds and prove that weak immersions that are critical points of such energies are analytic in any given local harmonic chart. Because of the…
It is a review paper. General relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary arbitrary curved background…