Related papers: Fractional Skyrmion molecules in a $\mathbb{C}P^{N…
The dense compact star matter is studied by using the skyrmion crystal approach. The chiral effective theory used includes the lightest scalar meson, the lowest-lying vector mesons as well as pions. Consistency with the vector manifestation…
Optical topologies in the form of Skyrmions have attracted significant interest of late, where their integer Skyrmion number has been shown to be robust to complex media. Here we create the first fractional Skyrmions by structuring light as…
Skyrmions with a realistic value of the pion mass parameter are expected to be quite compact structures, but beyond baryon number B=8 only a few examples are known. The largest of these is the cubically symmetric B=32 Skyrmion which is a…
Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz equation for ferromagnets with the Dzyaloshinskii-Moriya (DM) interaction, characterized by a topological number. We study the profile of an axially symmetric…
Topologically nontrivial field configurations called "baby skyrmions" behave like particles and give origins to the field of skyrmionics that promises racetrack memory and other technological applications. Unraveling the non-equilibrium…
The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…
We develop a formalism wherein the solution of the equations of equilibrium for a self-gravitating, magnetized interstellar cloud may be accomplished analytically, under the only hypotheses that (a) the cloud is scale-free, and (b) is…
In this paper we study fractional as well as semi-local Chern-Simons vortices in G = U(1) x SO(2M) and G = U(1) x USp(2M) theories. The master equations are solved numerically using appropriate Ansatze for the moduli matrix field. In the…
The broken planar Skyrme model is a theory that breaks global O(3) symmetry to the dihedral group D_N. It has been shown that the single soliton solution is formed of N constituent parts, named partons, that are topologically confined. The…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
We develop a one-parameter family of static baby Skyrme models that do not require a potential term to admit topological solitons. This is a novel property as the standard baby Skyrme model must contain a potential term in order to have…
We show that skyrmions arising from compact five dimensional models have stable sizes. We numerically obtain the skyrmion configurations and calculate their size and energy. Although their size strongly depends on the magnitude of localized…
Soliton solutions with cylindrical symmetry are investigated within the nonlinear $\sigma $-model disregarding the Skyrme-stabilization term. The solitons are stabilized by quantization of collective breathing mode and collapse in the…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one-phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions $n\geq3$ is completely open. In…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We construct sphaleron solutions with discrete symmetries in Yang-Mills-Higgs theory coupled to a dilaton. Related to rational maps of degree N, these platonic sphalerons can be assigned a Chern-Simons number Q=N/2. We present sphaleron…
Previous results on multi-charged Baby Skyrmion solutions have pointed to a modular structure, comprised of charge two rings and single charge one Skyrmions, which combine to form higher charged structures. In this paper we present…
A numerical study of fractional Camassa-Holm equations is presented. Smooth solitary waves are constructed numerically. Their stability is studied as well as the long time behavior of solutions for general localised initial data from the…
We study static solutions of the standard Skyrme model with a pion mass. Using approximately $10^5$ pseudo-random initial configurations made of single Skyrmions in the non-symmetrized product Ansatz and an automatic detection of repeated…