Related papers: Integrable geometry and Soliton equations in 2+1 d…
The soliton technique is applied to the 5D static Einstein-Maxwell equations, and an infinite number of solutions are explicitly obtained. We study the rod structure of 2-soliton solutions and we show that the 5D Reissner-Nordstrom solution…
The bi-Hamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general bi-Hamiltonian…
The strict relation between some class of multiboson hamiltonian systems and the corresponding class of orthogonal polynomials is established. The correspondence is used effectively to integrate the systems. As an explicit example we…
This is the first of a two-part work on Kleiman's iterated multiple point spaces. We show general properties of these spaces, leading to explicit equations describing them for maps (of any corank) between complex manifolds. We also describe…
This review paper is a continuation of hep-th/0012145 and it deals primarily with noncommutative ${\mathbb R}^{d}$ spaces. We start with a discussion of various algebras of smooth functions on noncommutative ${\mathbb R}^{d}$ that have…
We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol'nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the…
he Singular Manifold Method is presented as an excellent tool to study a 2+1 dimensional equation in despite of the fact that the same method presents several problems when applied to 1+1 reductions of the same equation. Nevertheless these…
We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
In 1+1-dimensions, an extension of the canonical solitonic Dym equation has previously been derived both in a geometric torsion evolution context and in the analysis of peakon solitonic phenomena in hydrodynamics. Here, a novel…
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the equations.
Some of the most important classes of surfaces in projective 3-space are reviewed: these are isothermally asymptotic surfaces, projectively applicable surfaces, surfaces of Jonas, projectively minimal surfaces, etc. It is demonstrated that…
An expository approach is given on the relationship between algebraic and geometric approaches to properties of isometries in the plane and the 2-sphere.
An overview of some of the recent developments in the theory of valuations on convex sets and its generalizations to manifolds is given. The exposition is focused towards applications to integral geometry; several of such applications are…
Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems.…
This study is an extented analogue to conformal geometry of the paper given by [14]. Also, the geometric and physical results related to bi-para-conformal-dynamical systems are also presented.
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…
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
This paper studies isometric immersions of space forms by means of a hierarchy of finite dimensional integrable systems in Lax form on loop algebras.
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…