Related papers: On Affine Orbifold Nets Associated with Outer Auto…
In many physical applications solitons propagate on supports whose topological properties may induce new and interesting effects. In this paper, we investigate the propagation of solitons on chains with a topological inhomogeneity generated…
This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…
We provide a proof of a formula conjectured in \cite{OU93} for some coefficients relevant in the principal vertex operator construction of a simply-laced affine algebra $\gh$. These coefficients are important for the study of the…
We discuss conditions under which an affine automorphism of a compact nilmanifold is almost automorphic, and the structure of such automorphisms from a dynamical point of view.
We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong XPM interaction, vector solitons with…
We give a new proof of Cartan's fixed point theorem using topological fixed point theory. For an odd dimensional, simply connected and complete manifold having non-positive curvature, we further prove that every isometry with finite order…
We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…
Given a two-dimensional conformal field theory with a global symmetry, we propose a method to implement an orbifold construction by taking orbits of the modular group. For the case of cyclic symmetries we find that this approach always…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
New single soliton solutions to the affine Toda field theories are constructed, exhibiting previously unobserved topological charges. This goes some of the way in filling the weights of the fundamental representations, but nevertheless…
We theoretically investigate the stability and dynamics of self-channelled beams that form via nonlocal optomechanical interactions in dual-nanoweb microstructured fibers. These "optomechanicons" represent a novel class of spatial soliton.
We construct a compact convex generating set $\mathcal{C}_n$ of the moduli set of closed connected projective special real manifolds of fixed dimension $n$. We show that a closed connected projective special real manifold corresponds to an…
We study orbit closures and stationary measures for groups of automorphisms of $p$-adic affine surfaces.
The concept of soliton, in its most general version, allows us to find canonical or distinguished elements on any set provided with an equivalence relation and an `optimal' tangent direction at each point. We study in this paper solitons on…
In this article, we study the twisting procedure of orbifold cohomology. We introduce local system and construct twisted orbifold cohomology. Then, we generalize Vafa-Witten's notion of discrete torsion to general orbifold and examine its…
We analyze string theory backgrounds that include different kinds of orientifold planes and map out a natural correspondence to (twisted) affine Kac-Moody algebras. The low-energy description of specific BPS states in these backgrounds…
Nonlinear properties of a multi-layer stack of graphene sheets are studied. It is predicted that such a structure may support dissipative plasmon-solitons generated and supported by an external laser radiation. Novel nonlinear equations…
We describe different types of self-trapped optical beams carrying phase dislocations, including vortex solitons and ring-like soliton clusters. We demonstrate numerically how to create such nonlinear singular beams by the interaction of…
We construct examples of normal affine varieties X of dimension greater than or equal to 4 such that the group of special automorphisms SAut(X) acts on X with an open orbit O and the complement X\O has codimension one.
We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of…