Related papers: Exact knot solutions in a generalized Skyrme-Fadde…
We study soliton solutions of the Nicole model - a non-linear four-dimensional field theory consisting of the CP^1 Lagrangian density to the non-integer power 3/2 - using an ansatz within toroidal coordinates, which is indicated by the…
We study cosmological inflation in the Einstein gravity model, where additionally the Gauss-Bonnet term non-minimally coupled to a scalar field is included. We prove that inflationary solutions of exponential and power-law types are…
A family of real Hamiltonian forms (RHF) for the special class of affine 1+1 - dimensional Toda field theories is constructed. Thus the method, proposed in [Mikhailov;1981] for systems with finite number of degrees of freedom is generalized…
In many applications to finite Fermi-systems, the pairing problem has to be treated exactly. We suggest a numerical method of exact solution based on SU(2) quasispin algebras and demonstrate its simplicity and practicality. We show that the…
This paper describes a natural one-parameter family of generalized Skyrme systems, which includes the usual SU(2) Skyrme model and the Skyrme-Faddeev system. Ordinary Skyrmions resemble polyhedral shells, whereas the Hopf-type solutions of…
A new class of non-linear O(3) models is introduced. It is shown that these systems lead to integrable submodels if an additional integrability condition (so called the generalized eikonal equation) is imposed. In the case of particular…
The Skyrme-Faddeev system, a modified O(3) sigma model in three space dimensions, admits topological solitons with nonzero Hopf number. One may learn something about these solitons by considering the system on the 3-sphere of radius R. In…
We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use the Vassiliev invariants for knots, proving that these are…
Numerical methods are used to compute sphaleron solutions of the Skyrme model. These solutions have topological charge zero and are axially symmetric, consisting of an axial charge n Skyrmion and an axial charge -n antiSkyrmion (with n…
We consider a model of scalar field with non minimal kinetic and Gauss Bonnet couplings as a source of dark energy. Based on asymptotic limits of the generalized Friedmann equation, we impose restrictions on the kinetic an Gauss-Bonnet…
A family of modified Nicole models is introduced. We show that for particular members of the family a topological soliton with a non-trivial value of the Hopf index exists. The form of the solitons as well as their energy and topological…
The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf…
A class of exact solutions of the Faddeev model, that is, the modified SO(3) nonlinear sigma model with the Skyrme term, is obtained in the four dimensional Minkowskian spacetime. The solutions are interpreted as the isothermal coordinates…
A topological lower bound on the Skyrme energy which depends explicity on the pion mass is derived. This bound coincides with the previously best known bound when the pion mass vanishes, and improves on it whenever the pion mass is…
We present a direct connection between torus knots and Hopfions by finding stable and static solutions of the extended Faddeev-Skyrme model with a ferromagnetic potential term. (P,Q)--torus knots consisting of |Q| sine-Gordon kink strings…
We examine nonlinear sigma models, in particular the Skyrme model with a twist (the twisted Skyrmion string), which comprises a vortex solution with an added dependence on a twist term $mkz$, where $z$ is the vertical coordinate. The…
We look at properties of vortex solutions of the extended CP^N Skyrme-Faddeev model. We show that only holomorphic solutions of the CP^N model are also solutions of the Skyrme-Faddeev model. As the total energy of these solutions is…
The Skyrme-Faddeev model has planar soliton solutions with target space $\mathbb{C}P^N$. An Abelian Chern-Simons term (the Hopf term) in the Lagrangian of the model plays a crucial role for the statistical properties of the solutions.…
The gauge equivalent formulation of the Faddeev-Skyrme model is used for the study of the quantum theory. The rotational quantum excitations around the soliton solution of Hopf number unity are investigated by the method of collective…
Using Painlev\'e analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the (1+1)-dimensional complex cubic and quintic Swift-Hohenberg equations. We consider both standard and generalized…