相关论文: Six-dimensional spaces defined by the equations of…
Eight-dimensional the Ricci-flat space defined by solutions of the Kadomtsev-Petviashvili equatin is presented. Its properties are discussed
The examples of ten-dimensional vacuum Einstein spaces composed of four-dimensional Einstein spaces and six-dimensional Ricci-flat base space defined by the solutions of the Korteveg de-Vries equation are constructed.
An examples of multidimensional the Ricci-flat spaces defined by nonlinear differential equations are constructed. Their properties are discussed.
We consider the one dimensional periodic complex valued mKdV, which corresponds to the first equation above cubic NLS in the associated integrable hierarchy. Our main result is the construction of a sequence of invariant measures supported…
A symmetry classification is performed for a class of differential-difference equations depending on 9 parameters. A 6-parameter subclass of these equations is an integrable discretization of the Krichever-Novikov equation. The dimension…
In this note we find the metrics of 6-dimensional h-spaces of the [3(21)], [(32)1], [(321)] types and then determine the quadratic first integrals of the geodesic equations of these h-spaces.
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are…
Metric spaces $(X, d)$ are ubiquitous objects in mathematics and computer science that allow for capturing (pairwise) distance relationships $d(x, y)$ between points $x, y \in X$. Because of this, it is natural to ask what useful…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
We consider the WDVV associativity equations in the four dimensional case. These nonlinear equations of third order can be written as a pair of six component commuting two-dimensional non-diagonalizable hydrodynamic type systems. We prove…
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated…
We present a metric for which Einstein's field equations in vacuum generate the Kortweg-de Vries (KdV) equation and thus its $N$-soliton solutions solve the vacuum equations. The metric of the one soliton solution has been investigated and…
The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical…
An examples of Monge-Ampere equations connected with six-dimensional generalization of the Plebanski four-dimensional space are considered. Their particular solutions are constructed.
We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively…
The space of functions A over the phase space of KdV-hierarchy is studied as a module over the ring D generated by commuting derivations. A D-free resolution of A is constructed by Babelon, Bernard and Smirnov by taking the classical limit…
One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this…
Pairs of metrics in a three-dimensional linear vector space are considered, one of which is a Minkowski type metric with the signature (+,-,-). Such metric pairs are classified and canonical presentations for them in each class are…
Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\"ahler metrics $g_K$ is constructed, defined on an…
We revisit the symmetry structure of integrable PDEs, looking at the specific example of the KdV equation. We identify 4 nonlocal symmetries of KdV depending on a parameter, which we call generating symmetries. We explain that since these…