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Irina Yehorchenko

Publications and source records attributed to Irina Yehorchenko.

15 recordsLinked to original sources
arXiv2018

Invariants for sets of vectors and rank 2 tensors, and differential invariants for vector functions

We outline an algorithm for construction of functional bases of absolute invariants under the rotation group for sets of rank 2 tensors and vectors in the Euclidean space of arbitrary dimension. We will use our earlier results for symmetric tensors and add results for sets including antisymmetric tensors of rank 2. That allowed, in particular, constructing of functional bases of differential invariants for vector functions, in particular, of first-order invariants of Poincaré algebra (invariance algebra of Maxwell equations for vector potential).

math-ph↗
arXiv2017

General Solution for a Coupled System of Eikonal Equations in Two Space Variables

A general solution for a coupled system of eikonal equations u_μu_μ= 0, v_μv_μ= 0, u_μv_μ= 1 is presented, where lower indices designate derivatives, μ= 0, 1, 2 and summation is implied over the repeated indices. This solution is of interest by itself due to wide applications of the eikonal equations, but the system considered also appears to be part of the reduction conditions for many equations of mathematical physics. We describe in detail the procedure that allowed obtaining of the general solution using hodograph and contact transformations of the initial system, however, we omit here special case when the system is equivalent to a system for one space dimension or to a system for one dependent function. The procedure used allowed also obtaining of the general solution for a coupled system of the eikonal and Hamilton-Jacobi equation.

math-ph↗
arXiv2014

Ansatzes and exact solutions for nonlinear Schrodinger equations

We consider construction of ansatzes for nonlinear Schrodinger equations in three space dimensions and arbitrary nonlinearity, and conditions of their reduction to ordinary differential equations. Complete description of ansatzes of certain types is presented. We also discuss the relationship between solutions, and both Lie and conditional symmetry of these equations.

math-ph↗
arXiv2011

Differential Invariants and Hidden Symmetry

We describe some classes of PDE that display hidden symmetry, with reduced equations having additional symmetry operators compared to the initial equations. Relations between the concepts of hidden and conditional symmetry, and between hidden symmetry and equivalence of classes of equations, is discussed. In particular, we describe equations having hidden and conditional symmetry under rotations and boosts in the Lorentz and Euclid groups.

math-ph↗
arXiv2009

Reduction of non-linear d'Alembert equations to two-dimensional equations

We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the reduced equations represent interesting classes of two-dimensional parabolic, hyperbolic and elliptic equations. Ansatzes and methods used for reduction of the d'Alembert (n-dimensional wave) equation can be also used for arbitrary Poincare-invariant equations. This seemingly simple and partial problem involves many important aspects in the studies of the PDE.

math-ph↗
arXiv2006

Reduction of multidimensional non-linear d'Alembert equations to two-dimensional equations: ansatzes, compatibility of reduction conditions

We study conditions of reduction of multidimensional wave equations - a system of d'Alembert and Hamilton equations. Necessary conditions for compatibility of such reduction conditions are proved. Possible types of the reduced equations and ansatzes are described. We also provide a brief review of the literature with respect to compatibility of the system of d'Alembert and Hamilton equations and construction of solutions for the nonlinear d'Alembert equation.

math-ph↗
arXiv2006

Differential Invariants for Infinite-Dimensional Algebras

We present an approach for construction of functional bases of differential invariants for some infinite-dimensional algebras with coefficients of generating operators depending on arbitrary functions. An example for the infinite-dimensional Poincare-type algebra is given.

math-ph↗