Related papers: Singular soliton solution in the Chern-Simons-CP(1…
We construct some intrinsically defined discrete model of the magnetic Laplacian. The existence and uniqueness of solutions of the Dirichlet problem for the difference Poisson type equation are proved. We study in detail properties of the…
We study the effect of a (3+1)-dimensional Chern-Simons electrodynamics on the equations governing the dynamics of magnetized plasma and fields. In this model, the Chern-Simons (CS) part consists of a dynamical pseudo-scalar field whose…
We verify the existence of radially symmetric first-order solitons in a gauged $CP(2)$ scenario in which the dynamics of the Abelian gauge field is controlled by the Maxwell-Chern-Simons action. We implement the standard…
We consider solitary wave solutions to the Dirac--Coulomb system both from physical and mathematical points of view. Fermions interacting with gravity in the Newtonian limit are described by the model of Dirac fermions with the Coulomb…
We study the domain wall soliton solutions in the relativistic self-dual Maxwell Chern-Simons model in 1+1 dimensions obtained by the dimensional reduction of the 2+1 model. Both topological and nontopological self-dual solutions are found…
The $O(3)$ nonlinear sigma model with its $U(1)$ subgroup gauged, where the gauge field dynamics is solely governed by a Chern-Simons term, admits both topological as well as nontopological self-dual soliton solutions for a specific choice…
I analyze the one-dimensional, cubic Schr\"odinger equation, with nonlinearity constructed from the current density, rather than, as is usual, from the charge density. A soliton solution is found, where the soliton moves only in one…
We consider a uniaxial planar ferromagnet coupled minimally to an Abelian Chern-Simons gauge field and study self-dual solitons which saturate the Bogomol'nyi bound. We find a rich structure of rotationally symmetric static soliton…
In this work, we investigate the solutions of vortices in the O(3)-sigma model with the gauge field governed by the Chern-Simons term and subject to a hyperbolic self-dual potential. We show that this model admits both topological and…
We present a new type of a thermodynamically stable magnetic state at interfaces and surfaces of chiral magnets. The state is a soliton solution of micromagnetic equations localized in all three dimensions near a boundary and contains a…
Self-dual vortex solutions are studied in detail in the generalized abelian Higgs model with independent Chern-Simons interaction. For special choices of couplings, it reduces to a Maxwell-Higgs model with two scalar fields, a…
In this paper we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the…
In this article are computed magnetic solutions of Einstein Maxwell Chern-Simons theory coupled to a dilaton-like scalar field. These solutions are computed by applying a space-time duality suggested by the author to known electric…
We present a self-dual parity-invariant $U(1) \times U(1)$ Maxwell-Chern-Simons scalar $\text{QED}_3$. We show that the energy functional admits a Bogomol'nyi-type lower bound, whose saturation gives rise to first order self-duality…
In mean field approximation, we study a chiral soliton of the linear sigma model with two flavors at finite temperature and density. The stable soliton solutions are calculated with some appropriate boundary conditions. Energy and radius of…
The self-dual Chern-Simons solitons under the influence of the quantum potential are considered. The single-valuedness condition for an arbitrary integer number $N \ge 0$ of solitons leads to quantization of Chern-Simons coupling constant…
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with…
We consider the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov--Bohm solenoid field and a collinear uniform magnetic field). Using von Neumann's theory of the self-adjoint extensions of symmetric operators,…
In this paper, we consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a…
We study dynamics of non-relativistic Chern-Simons solitons, both in the absence and in the presence of external fields. We find that a phase, related to the $1$-cocyle of the Galileo group, must be included to give the correct dynamical…