Related papers: Discrete Skyrmions in 2+1 and 3+1 Dimensions
The existence of multidimensional lattice compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. By averaging over the period of the fast…
Discrete transformation for 3- waves problem is constructed in explicit form. Generalization of this system on the matrix case in three dimensional space together with corresponding discrete transformation is presented also.
Models of folding of a triangular lattice embedded in a discrete space are studied as simple models of the crumpling transition of fixed-connectivity membranes. Both the case of planar folding and three-dimensional folding on a…
There is a deformation of the ordinary differential calculus which leads from the continuum to a lattice (and induces a corresponding deformation of physical theories). We recall some of its features and relate it to a general framework of…
General topologically invariant microscopical expressions for quantum numbers of particle-like solitons ("skyrmions") are derived for a class of (2+1)D models. Skyrmions are either half-integer spin fermions with odd electric charge or…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
We study the physics of a single discrete gravitational extra dimension using the effective field theory for massive gravitons. We first consider a minimal discretization with 4D gravitons on the sites and nearest neighbor hopping terms. At…
We derive and discuss black-hole solutions to the gravitating O(3) $\sigma$ model in (2+1) dimensions. Three different kinds of static black holes are found. One of these resembles the static BTZ black hole, another is completely free of…
Intricate spin textures in helimagnets, identified as stable topological Skyrmions, were observed experimentally, where Skyrme lattice was supposed to exhibit symmetric structures in the ground state. We show the possibility of asymmetric…
In this paper, we develop discrete versions of Darboux transformations and Crum's theorems for two second order difference equations. The difference equations are discretised versions (using Darboux transformations) of the spectral problems…
We investigate a 3+1 dimensional toy model that exhibits spontaneous breakdown of chiral symmetry, both in a light-front (LF) Hamiltonian and in a Euclidean Schwinger-Dyson (SD) formulation. We show that both formulations are completely…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few…
Using numerical simulations, the stability and scattering properties of the O(3) model on a two-dimensional torus are studied. Its solitons are found to be unstable but can be stabilized by the addition of a Skyrme term to the Lagrangian.…
We investigate the formation of singularities in a baby Skyrme type energy model, which describes magnetic solitons in two-dimensional ferromagnetic systems. In presence of a diverging anisotropy term, which enforces a preferred background…
Collapse of a skyrmion due to the discreteness of a crystal lattice in isotropic two-dimensional ferro- and antiferromagnets has been studied analytically and by numerical solution of equations of motion for up to 2000 x 2000 classical…
We prove large-data local stability theorems for several spin models in two dimensions.
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
Effective estimates for the lattice point discrepancy of certain planar and three-dimensional domains. This paper provides estimates, with explicit constants, for the lattice point discrepancy of o-symmetric ellipse discs and ellipsoids in…
The investigation of magnetic solitons often relies on numerical modeling to determine key features such as stability, annihilation, nucleation, and motion. However, as soliton sizes approach atomic length scales, the accuracy of these…