Related papers: Knot Solitons
The O(3) sigma model in two spatial dimensions admits topological (Bogomol'nyi) lower bound on its energy. This paper proposes a lattice version of this system which maintains the Bogomol'nyi bound and allows the explicit construction of…
We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge $U(1)$-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and…
In this paper we review recent results on the existence of non-topological solitons in classical relativistic nonlinear field theories. We follow the Coleman approach, which is based on the existence of two conservation laws, energy and…
In this article, we propose a new approach for describing and understanding knots and links in a 3-manifold through the use of an embedded non-orientable surface. Specifically, we define a plat-like representation based on this…
We study the invariant of knots in lens spaces defined from quantum Chern-Simons theory. By means of the knot operator formalism, we derive a generalization of the Rosso-Jones formula for torus knots in L(p,1). In the second part of the…
Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsions. When the underlying algebra is $\mathbb{Z}[x]/(x^2)$,…
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…
Following our earlier work we argue in detail for the equivalence of the nonlinear $\sigma$ model with Hopf term at~$\theta=\pi/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $\sigma$ model and show the…
We introduce the self-dual abelian gauged $O(3)$ sigma models where the Maxwell and Chern-Simons terms constitute the kinetic terms for the gauge field. These models have quite rich structures and various limits. Our models are found to…
The defect-type solutions of a deformed $O(2N+1)$ linear sigma model with a real and $N$ complex fields in $(1+1)$-dimensional Minkowski spacetime are studied. All the solutions are analytically found for the $N=2$ case. Two types of…
The Boltzmann type kinetic equation for solitons in Nonlinear Schr\"{o}dinger equation has been constructed on the base of analysis of two soliton collision. Possible applications for Langmuir solitons in plasma and solitons in optic fiber…
In this paper we present some families of polynomials and use them to find, using the techniques in \cite{gma}, a defining polynomial for the $SL(2,\mathbb{C})$ character variety (as defined in \cite{cus}) of the torus knots of type $(m,2)$…
It is shown that the four trefoil solitons that are described by the irreducible representations D^{3/2}_{mm'} of the quantum algebra SL_q(2) (and that may be identified with the four families of elementary fermions…
We conjecture that the stable Khovanov homology of torus knots can be described as the Koszul homology of an explicit non-regular sequence of quadratic polynomials. The corresponding Poincare series turns out to be related to the…
We present a systematic classification of uncolored bonded knots with singularity number at most seven. Bonded knots provide a topological model for closed protein chains with intramolecular bridges, such as disulfide bonds. Following the…
The A-polynomial of a knot is defined in terms of SL(2,C) representations of the knot group, and encodes information about essential surfaces in the knot complement. In 2005, Dunfield-Garoufalidis and Boyer-Zhang proved that it detects the…
We argue that an oscillatory motion of impurity-pinned solitons may occur in layered antiferromagnetic compounds. The characteristic frequencies of these modes, that may be detected by resonance or inelastic neutron scattering, are…
Knots in the Chern-Simons field theory with Lie super gauge group $SU\left(M|N\right) $ are studied, and the $% S_{L}\left(\alpha,\beta,z\right) $ polynomial invariant with skein relations are obtained under the fundamental representation…
The interrelation between Ferreira's Hopf solitons of a conformal nonlinear $\sigma$ model and the electromagnetic knots found by Ra$\tilde{\rm{n}}$ada et al. is investigated. It is shown that the electromagnetic knots yield exact solutions…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…