Related papers: On the Soliton Geometry in Multidimensions
We consider solitonic solutions of coupled scalar systems, whose Lagrangian has a potential term (quasi-supersymmetric potential) consisting of the square of derivative of a superpotential. The most important feature of such a theory is…
We study the stability of multipole-mode solitons in one-dimensional thermal nonlinear media. We show how the sample geometry impacts the stability of mutlipole-mode solitons and reveal that the tripole and quadrupole can be made stable in…
Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry…
One considers the monistic conception of a geometry, where there is only one fundamental quantity (world function). All other geometrical quantities a derivative quantities (functions of the world function). The monisitc conception of a…
We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex…
The study of noncommutative solitons is greatly facilitated if the field equations are integrable, i.e. result from a linear system. For the example of a modified but integrable U(n) sigma model in 2+1 dimensions we employ the dressing…
"Light bullets" are multi-dimensional solitons which are localized in both space and time. We show that such solitons exist in two- and three-dimensional self-induced-transparency media and that they are fully stable. Our approximate…
Some relations between cohomological dimensions and depths of linked ideals are investigated and discussed by various examples.
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
This text is the extended version of a talk given at the conference Geometry, Topology, QFT and Cosmology hold from May 28 to May 30, 2008 at the Observatoire de Paris. We explore the notion of solder (or soldering form) in differential…
The motion of three-dimensional (3D) solitary waves and solitons in nonlinear crystal-like structures, such as photonic materials, is studied. It is demonstrated that collective excitations in these systems can be tailored to move in…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
A way to add an extra dimension is briefly discussed.
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
The relation between differential geometry of surfaces and some Heisenberg ferromagnet models is considered.
We analyze nonlinear collective effects near surfaces of semi-infinite periodic systems with multi-gap transmission spectra and introduce a novel concept of multi-gap surface solitons as mutually trapped surface states with the components…
We discuss various phenomena of tangency in projective and convex geometry.
We review recent results and ongoing investigations of the symplectic and Poisson geometry of derived moduli spaces, and describe applications to deformation quantization of such spaces.