Related papers: Isolated Skyrmions in the $CP^2$ nonlinear $\sigma…
On the two-dimensional non-linear $\Sigma$-model describing a ferromagnet with Dzyaloshinskii-Moriya interaction, we build three families of exact static solutions depending on a single Cartesian variable. One of them describes a clockwise…
We consider the (2+1)-dimensional gauged Heisenberg ferromagnet model coupled with the Chern-Simons gauge fields. Self-dual Chern-Simons solitons, the static zero energy solution saturating Bogomol'nyi bounds, are shown to exist when the…
We give a succinct summary of the recently discovered solvable models of magnetic skyrmions in two dimensions, and of their general solutions. The models contain the standard Heisenberg term, the most general translation invariant…
We investigate a coupled system of a Dirac particle and a pseudoscalar field in the form of a soliton in (1+1) dimensions and find some of its exact solutions numerically. We solve the coupled set of equations self-consistently and…
We find approximate solutions for the two-dimensional non-linear {\Sigma}-model with Dzyalioshinkii-Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in…
We develop a multiscale approach to magnetoelectric effects, bridging atomistic and continuum models, with all parameters determined from ab initio electronic structure calculations. We show that the parameters of the model are equivalent…
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any…
We demonstrate that the commonly known concept, which treats solitons as nonsingular solutions produced by the interplay of nonlinear self-attraction and linear dispersion, may be extended to include modes with a relatively weak singularity…
We derive the long-wavelength non-linear sigma model for a two-dimensional Heisenberg system in the presence of the Dzyaloshinskii-Moriya and pseudodipolar interactions. We show that the system is a non-conventional easy-axis…
The unusual magnetic behaviour of helimagnet MnSi, noticed in recent years, prompted the suspicion that the magnetic states arising in such crystals are of topological nature. Recent experiments based on the topological Hall effect…
An integrable two-dimensional system related to certain fermion-soliton systems is studied. The self-consistent solutions of a static version of the system are obtained by using the tau function approach. The self-consistent solutions…
A study of the dynamical two-dimensional (2D) nonlinear response of the dimerized spin-$1{/}2$ chain to external electric fields is presented. The coupling of the spin system to those fields is set to arise from the inverse…
We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary…
It is shown that a gauged nonlinear $O(3)$ sigma model with anomalous magnetic moment interaction in $2+1$ dimensions is exactly integrable for static, self-dual field configurations. The matter fields are exactly equivalent to those of the…
We investigate some fundamental features of a class of non-linear relativistic lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space…
We study $\mathbb{C}P^2$ Skyrmion crystals in the ferromagnetic SU(3) Heisenberg model with a generalization of the Dzyaloshinskii-Moriya interaction and the Zeeman term. The model possesses two different types of Skyrmion crystals with…
We perform the dimensional reduction of the nonrelativistic CP(1) model coupled to an Abelian Chern-Simons gauge field in the self-dual limit, and investigate the soliton and domain wall solutions of the emerging 1+1 dimensional self-dual…
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schr\"odinger equation introduced by Zakharov and studied…
In this paper we link the physics of topological nonlinear {\sigma} models with that of Chern-Simons insulators. We show that corresponding to every 2n-dimensional Chern-Simons insulator there is a (n-1)-dimensional topological nonlinear…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…