Related papers: On the Soliton Geometry in Multidimensions
Various soliton-obstruction systems have been studied from analytical perspective. We have used collective coordinate to approach the dynamics of solitons as they meet a potential obstruction in a form of square barriers and holes for three…
We derive exact analytical solutions describing multi-soliton complexes and their interactions on top of a multi-component background in media with self-focusing or self-defocusing Kerr-like nonlinearities. These results are illustrated by…
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…
Application of the noncommutative geometry to several physical models is considered.
We study (2+1)-dimensional multicomponent spatial vector solitons with a nontrivial topological structure of their constituents, and demonstrate that these solitary waves exhibit a symmetry-breaking instability provided their total…
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
Multimodal normal incestual systems are investigated in terms of multiple categories. The different sorted composition of operators are exhibited as 2-cells in multiple categories built up from 2-categories giving rise to different axioms.…
In two space-time dimensions a class of classical multicomponent scalar field theories with discrete, in general non-Abelian global symmetry is considered. The corresponding soliton solutions are given for the cases of 2, 3, and 4…
In this work, we present a general procedure, which is able to generate new exact solitonic models in 1+1 dimensions, from a known one, consisting of two coupled scalar fields. An interesting consequence of the method, is that of the…
Geometrical aspects of a perfect fluid spacetime are described in terms of different curvature tensors and $\eta$-Ricci and $\eta$-Einstein solitons in a perfect fluid spacetime are determined. Conditions for the Ricci soliton to be steady,…
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
This paper is concerned with the generalized Davey-Stewarston system in two dimensional space. Existence and stability of small solitons are proved by solving two correlative constrained variational problems and spectrum analysis. In…
Two-dimensional dilaton gravity coupled to a Klein-Gordon matter field with a quartic interaction term is considered. The theory has a classical solution which exhibits black hole formation by a soliton. The geometry of black hole induced…
The first results, both positive and negative, recently obtained in the area of constructing stationary spinning solitons in flat Minkowski space in 3+1 dimensions are discussed.
In the previous article (J. Geom. Phys. {\bf 43} (2002) 146), we show the hyperelliptic solutions of a loop soliton as a study of a quantized elastica. This article gives some functional relations in a loop soliton as a quantized elastica.
Motivated by strong desire to understand the natural geometry of moduli spaces of hyperbolic monopoles, we introduce and study a new type of geometry: pluricomplex geometry. It is a generalisation of hypercomplex geometry: we still have a…
Summary talk given at the 24th International Symposium on Multiparticle Dynamics, Italy, September 1994 -- This summary talk only reviews a small sample of topics featured at this symposium: 1. Introduction 2. The Geometry and Geography of…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity,…