Related papers: The search for solitons on homogeneous spaces
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
We report on the status of our search for quasi-topological solitons of various dimensions in realistic field theoretical models of condensed matter and of elementary particle physics.
Left-invariant Cotton solitons on homogeneous manifolds are determined. Moreover, algebraic Cotton solitons are studied providing examples of non-invariant Cotton solitons, both in the Riemannian and Lorentzian homogeneous settings.
For a polygon in Euclidean space we consider a transformation T which is obtained by applying the midpoints polygon construction twice and using an index shift. For a closed polygon this is a curve shortening process. A polygon is called…
We develop a general approach to study geometric flows on homogeneous spaces. Our main tool will be a dynamical system defined on the variety of Lie algebras called the bracket flow, which coincides with the original geometric flow after a…
We develop a general theory of spatial solitons in a liquid crystalline medium exhibiting a nonlinearity with an arbitrary degree of effective nonlocality. The model accounts the observability of "accessible solitons" and establishes an…
We describe the holonomy algebras of all canonical connections of homogeneous structures on real hyperbolic spaces in all dimensions. The structural results obtained then lead to a determination of the types, in the sense of Tricerri and…
A general approach allowing to find the analytical expressions for equilibrium magnetic structures in small and flat magnetic nano-sized cylinders of arbitrary shape made of soft magnetic material is presented. The resulting magnetization…
Solitons, as coherent structures that maintain their shape while traveling at constant velocity, are ubiquitous across various branches of physics, from fluid dynamics to quantum fields. However, it is within the realm of optics where…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
In this paper, we completely classify conformal solitons on pseudo-Riemannian hypersurfaces in pseudo-Euclidean spaces arisen from the position vector field. In particular, the classification of Yamabe solitons on pseudo-Riemannian…
We present a general review of the dynamics of topological solitons in 1 and 2 dimensions and then discuss some recent work on the scattering of various solitonic objects (such as kinks and breathers etc) on potential obstructions.
We propose a scheme to generate solitons in arbitrary dimensions, in a matter-wave interferometer, without the need of quantum degeneracy. In our setting, solitons emerge by balancing the single-particle dispersion with engineered…
We describe the holonomy algebras of all canonical connections and their action on complex hyperbolic spaces $\mathbb{C}\mathrm{H}(n)$ in all dimensions ($n\in\mathbb{N}$). This thorough investigation yields a formula for all Kahler…
Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons and phase solitons have been…
This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…
We show how to view the equations for a cohomogeneity one Ricci soliton as a Hamiltonian system with a constraint. We investigate conserved quantities and superpotentials, and use this to find some explicit formulae for Ricci solitons not…
We consider the existence of cohomogeneity one solitons for the isometric flow of $G_2$-structures on the following classes of torsion-free $G_2$-manifolds: the Euclidean $R^7$ with its standard $G_2$-structure, metric cylinders over…
The concept of the moduli space allows for a simple, universally applicable description of the low-energy dynamics of topological solitons. This description is remarkably insensitive to the properties of the underlying theory, whose details…
The existence of solitons -- stable, long-lived, and localized field configurations -- is a generic prediction for ultralight dark matter. These solitons, known by various names such as boson stars, axion stars, oscillons, and Q-balls…