Eight-dimensional Ricci-flat space related with the KP equation
Eight-dimensional the Ricci-flat space defined by solutions of the Kadomtsev-Petviashvili equatin is presented. Its properties are discussed
nlin.SI↗
arXiv subjects
Valery Dryuma
Publications and source records attributed to Valery Dryuma.
On Geometry of the Rössler system of equations
On a basis of theory of Riemann extension of the space of constant affine connection associated with the Rössler system of equations relations between its parameters are investigated.
nlin.SI↗
Riemann geometry in theory of the first order systems of equations
Theory of Riemann Extensions of the spaces with constant affine connection for the studying of the properties of nonlinear the first order systems of differential equations is proposed. Quadratic planar system of equations and the Lorenz system of equations are investigated in detail.
nlin.SI↗
10-Dim Einstein spaces made up on basis of 6-Dim Ricci-flat spaces and 4-Dim Einstein spaces
Some examples of ten-dimensional vacuum Einstein spaces made up on basis of four-dimensional Ricci-flat spaces and six-dimensional Ricci-flat spaces defined by solutions of the Sin-Gordon equation are constructed. The properties of geodesics for such type of the spaces are discussed
gr-qc↗
On the Riemann extension of rotating Mikowsky space-time metric
Some properties of eight-dimensional Riemann extension of Minkowsky space-time metric in rotating coordinate system are studied.
gr-qc↗
Is my ODE a Painleve equation in disguise?
Painleve equations belong to the class y'' + a_1 {y'}^3 + 3 a_2 {y'}^2 + 3 a_3 y' + a_4 = 0, where a_i=a_i(x,y). This class of equations is invariant under the general point transformation x=Phi(X,Y), y=Psi(X,Y) and it is therefore very difficult to find out whether two equations in this class are related. We describe R. Liouville's theory of invariants that can be used to construct invariant characteristic expressions (syzygies), and in particular present such a characterization for Painleve equations I-IV.
nlin.SI↗