Related papers: On the Soliton Geometry in Multidimensions

This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.

After a brief recapitulation of the general interest of parton densities, we discuss multiple hard interactions and multiparton distributions. We report on recent theoretical progress in their QCD description, on outstanding conceptual…

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.

In this small paper we bring together various open problems on geometric multidimensional continued fractions.

We discuss invariants in equivariant birational geometry.

We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are…

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more…

We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations…

We investigate the geometry of hyperbolic knots and links whose diagrams have a high amount of twisting of multiple strands. We find information on volume and certain isotopy classes of geodesics for the complements of these links, based…

We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most…

We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the Delzant polytope of a toric symplectic manifold.

The formalism for describing a metric and the corresponding scalar in terms of multipole moments has recently been developed for scalar-tensor theories. We take advantage of this formalism in order to obtain expressions for the observables…

We survey some recent developments in the asymptotic geometry of the Hitchin moduli space, starting with an introduction to the Hitchin moduli space and hyperk\"ahler geometry.

The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in…

In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.

We formulate the soliton equations on the lattice in terms of the reduced Moyal algebra which includes one parameter. The vanishing limit of the parameter leads to the continuous soliton equations.

Some intensive observables of the electronic ground state in condensed matter have a geometrical or even topological nature. In this Review I present the geometrical observables whose expression is known in a full many-body framework,…

The object of the present paper is to study some properties of (LCS)$_n$-manifolds whose metric is Yamabe soliton. We establish some characterization of (LCS)$_n$-manifolds when the soliton becomes steady. Next we have studied some certain…

Domain wall networks on the surface of a soliton are studied in a simple theory. It consists of two complex scalar fields, in (3+1)-dimensions, with a global U(1) x Z_n symmetry, where n>2. Solutions are computed numerically in which one of…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…