Related papers: On the Soliton Geometry in Multidimensions

Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.

Some aspects of multidimensional soliton geometry are considered.

A connection between differential geometry and soliton equations is discussed

Some aspects of the multidimensional soliton geometry are considered. The relation between soliton equations in 2+1 dimensions and the Self-Dual Yang-Mills and Bogomolny equations are discussed.

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…

Some aspects of the relation between differential geometry of curves and surfaces and multidimensional soliton equations is discussed. The connection between multidimensional soliton equations and Self-dual Yang-Mills equation is studied.

Some soliton equation in 2+1 dimensions and their 1+1 and/or dimensional integrable reductions are considered.

Some aspects of two-dimensional gravity coupled to matter fields, especially to the Sine-Gordon-model are examined. General properties and boundary conditions of possible soliton-solutions are considered. Analytic soliton-solutions are…

The connection between multidimensional soliton equations and three-dimensional Riemann space is discussed.

Various aspects of Supersymmetry in 1-dimensional systems are analyzed.

Recently it has been discovered that some nonlinear evolution equations in 2+1 dimensions, which are integrable by the use of the Spectral Transform, admit localized (in the space) soliton solutions. This article briefly reviews some of the…

A class of solenoids is considered, including some aspects in n (topological) dimensions, where one basically gets some fractal versions of tori.

We consider the properties of massive one particle states on a translation covariant Haag-Kastler net in Minkowski space. In two dimensional theories, these states can be interpreted as soliton states and we are interested in the existence…

In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold $(M, <, >)$. We then draw some geometric conclusions with the aid of the maximum principle.

We discuss several rigidity and flexibility phenomena in the context of Poisson geometry.

In Riemannian geometry, Ricci soliton inequalities are an important field of study that provide profound insights into the geometric and analytic characteristics of Riemannian manifolds. An extensive study of Ricci soliton inequalities is…

We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.

Soliton propagation dynamics under the presence of a complex potential are investigated. A large variety of qualitatively different potentials, including periodic, semi-infinite periodic and localized potentials, is considered. Cases of…

[Dedicated to Richard S. Hamilton on forty years of Ricci flow] Gradient Ricci solitons have garnered significant attention both as self-similar solutions and singularity models of the Ricci flow. This survey article starts with a list of…

In the present paper, a notion of M-basis and multi dimension of a multi vector space is introduced and some of its properties are studied.