Related papers: Noncommutative Solitons
The perturbation theory around the soliton fields of the sin-Gordon model is developed in the coset space. It is shown by explicit calculations that all corrections to the topological soliton contribution are canceled exactly.
We begin to study a sigma-model in which both the space-time manifold and the two-dimensional string world-sheet are made noncommutative. The most precise results apply to the case where both the space-time manifold and the two-dimensional…
We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…
The equations for the solitons arbitrarily rotating in the ordinary and isotopic space are obtained. The wave functions of the corresponding dynamic states in the quantum case are found. The generalized matrix of the moments of inertia is…
We review spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic…
Solitons, nonlinear particle-like excitations with inalterable properties (amplitude, shape, and velocity) as they propagate, are omnipresent in many branches of science---and in physics in particular. Flat-top solitons are a novel type of…
A covariant formalism for Moyal deformations of gauge theory and differential equations which determine Seiberg-Witten maps is presented. Replacing the ordinary product of functions by the noncommutative Moyal product, noncommutative…
We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocing cross-interactions. The general properties of the stationary states and their stability are investigated. The different scenarios…
The behavior of solitons in integrable theories is strongly constrained by the integrability of the theory, that is by the existence of an infinite number of conserved quantities that these theories are known to possess. As a result the…
A large class of solvable models of dilaton gravity in two space-time dimensions, capable of describing black hole geometry, are analyzed in a unified way as non-linear sigma models possessing a special symmetry. This symmetry, which can be…
In the recent work "Non-reciprocal topological solitons in active metamaterials" (see arXiv:2312.03544v1), for an analytical understanding of the system under consideration, the authors derive an ordinary differential equation for the…
We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected,…
We find the moduli space of multi-solitons in noncommutative scalar field theories at large theta, in arbitrary dimension. The existence of a non-trivial moduli space at leading order in 1/theta is a consequence of a Bogomolnyi bound obeyed…
We study the sine-Gordon measure defined on each homotopy class. The energy space decomposes into infinitely many such classes indexed by the topological degree $Q \in \mathbf{Z}$. Even though the sine-Gordon action admits no minimizer in…
We study the symmetries of the soliton spectrum of a pair of T-dual integrable models, invariant under global $SL(2)_q\otimes U(1)$ transformations. They represent an integrable perturbation of the reduced Gepner parafermions, based on…
The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional…
The noncommutative soliton is characterized by the use of the projection operators in non-commutative space. By using the close relation with the K-theory of $C^*$-algebra, we consider the variations of projection operators along the…
The Euclidean analogues of the sine-Gordon solitons are used as sources of the heterotic fivebrane solutions in the ten-dimensional heterotic string theory. Some properties of these soliton solutions are discussed. These solitons in…
We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the…
We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is…