Related papers: Notes on Riemann geometry and integrable systems. …
A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose fourth power is the identity, is considered. This structure acts as an isometry with respect to the metric. A Riemannian almost product manifold…
We consider a scenario where our universe is taken as a three-dimensional domain wall embedded in a five-dimensional Minkowski space-time, as originally proposed by Brito and collaborators [1]. We explore the existence of a richer class of…
Some assertions in harmonic analysis on the infinite dimensional torus are stated and their equivalence to Riemann hypothesis is proved.
The purpose of this paper is to extend the store of models able to support integrable defects by investigating the two-dimensional Boussinesq nonlinear wave equation. As has been previously noted in many examples, insisting that a defect…
For the rational, elliptic and trigonometric r-matrices, we exhibit the links between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral…
A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for…
Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.
We develop the theory of relative regular holonomic D-modules with a smooth complex manifold S of arbitrary dimension as parameter space, together with their main functorial properties. In particular, we establish in this general setting…
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis…
Let $p:X\longrightarrow M$ be a Riemann domain over a connected $n$-dimensional complex submanifold $M$ of $\mathbb C^N$ and let $\mathcal F\subset\mathcal O(X)$ be such that $p\in\mathcal F^N$. Our aim is to discuss relations between the…
Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases of these spaces arise as moduli spaces of semistable…
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in…
We study the spatial structure of 1/4 BPS solitons in 4 dimensional N=4 gauge theory. A weak binding approximation is used where the soliton is made of several "ingredient" particles. Some spatial moduli are described which are not…
This study aims to investigate the interactions of solitons with an external force within the framework of the Schamel equation, both asymptotically and numerically. By utilizing asymptotic expansions, we demonstrate that the soliton…
The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing,…
This paper studies the situation when two 4-dimensional Lorentz manifolds (that is, space-times) admit the same (unparametrised) geodesics, that is, when they are projectively related. A review of some known results is given and then the…
We discuss the relation between Liouville theory and the Hitchin integrable system, which can be seen in two ways as a two step process involving quantization and hyperkaehler rotation. The modular duality of Liouville theory and the…
In this paper we present soliton solutions of two coupled nonlinear Schodinger equations modulated in the bspace and time. The approach allows us to obatin solitons with large variety of solutions depending on the nonlinearity and the…
We describe an approach to construct multi-soliton asymptotic solutions for non-integrable equations. The general idea is realized in the case of three waves and for the KdV-type equation with nonlinearity $u^4$. A brief review of…
We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…