Related papers: Exact knot solutions in a generalized Skyrme-Fadde…
Class of exact solutions of the Skyrme and the Faddeev model are presented. In contrast to previously found solutions, they are produced by the interplay of the two terms in the Lagrangians of the models. They are not solitonic but of wave…
Hopf solitons in the Skyrme-Faddeev system on $R^3$ typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3-manifold M, and the energy functional consists only of the…
We analytically construct vortex solutions in the integrable sector of the extended Skyrme-Faddeev model. The solutions are holomorphic type which satisfy the zero curvature condition. For the model parameter $\beta e^2=1$ there is a lump…
Regarding the Skyrme-Faddeev model on $\mathbb R^3$ as a $\mathbb C \mathbb P^1$ sigma model, we propose $\mathbb C \mathbb P^n$ sigma models on $\mathbb R^{2n+1}$ as generalisations which may support finite energy Hopfion solutions in…
We study the issue of stability of static soliton-like solutions in some non-linear field theories which allow for knotted field configurations. Concretely, we investigate the AFZ model, based on a Lagrangian quartic in first derivatives…
The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the…
We observe that the Faddeev-Skyrme model emerges as a low-energy limit of scalar QED with two charged scalar fields and a selfinteraction potential of a special form (inspired by supersymmetric QCD). Then we discuss possible Hopf solitons…
We report on the presence of families of exact solutions for a complex scalar field that behaves according to the rules of discrete $Z_N$ symmetry. Since the family of models is exactly solved, the results appear to be of interest to…
The extended Skyrme-Faddeev model possesses vortex solutions in a (3+1) dimensional Minkowski space-time with target space $CP^N$. They have finite energy per unit of length and contain waves propagating along vortices with the speed of…
Recently, Hirayama and Yamashita have presented an ansatz that allows us to construct a class of solutions for the SU(2) Skyrme model. Though these solutions are not solitonic, they provide us with an example on how the plane wave solutions…
The complex eikonal equation in $(3+1)$ dimensions is investigated. It is shown that this equation generates many multi soliton configurations with arbitrary value of the Hopf index. In general, these eikonal hopfions do not have the…
Recently it has been shown that there exists a sector within the Faddeev-Niemi model for which the equations of motion may be reduced to first order equations. However, no solutions to that sector have been given. It is not even known…
Simple physics ideas are used to derive an exact expression for a flat connection on the complement of a torus knot. The result is of some mathematical importance in the context of constructing representations of the knot group -- a…
We identify higher-charge configurations that satisfy Euler-Lagrange equations for the (strong coupling limit of) Faddeev-Hopf model, by means of adequate changes of the domain metric and a reduction technique based on $\alpha$-Hopf…
Generalized Aratyn-Ferreira-Zimerman O(3) nonlinear sigma model with a particular symmetry breaking term, so-called dielectric function, is discussed. Static multi-soliton configurations with finite energy and nontrivial Hopf index are…
We construct new solutions of the Faddeev-Skyrme model with a symmetry breaking potential admitting $S^1$ vacuum. It includes, as a limiting case, the usual $SO(3)$ symmetry breaking mass term, another limit corresponds to the potential…
Hopf solitons in the Skyrme-Faddeev model -- S^2-valued fields on R^3 with Skyrme dynamics -- are string-like topological solitons. In this Letter, we investigate the analogous lattice objects, for S^2-valued fields on the cubic lattice Z^3…
We introduce a new family of quasi-exactly solvable generalized isotonic oscillators which are based on the pseudo-Hermite exceptional orthogonal polynomials. We obtain exact closed-form expressions for the energies and wavefunctions as…
The Faddeev-Hopf model [1] supporting Hopfions was shown to emerge in the low-energy limit of four-dimensional scalar quantum electrodynamics (QED) with two charged scalar fields [2, 3]. Faddeev and Noemi conjectured that the Hopfions and…
We study a modified version of the Ginzburg-Landau model suggested by Ward and show that Hopfions exist in it as stable static solutions, for values of the Hopf invariant up to at least 7. We also find that their properties closely follow…