相关论文: Invariants of differential equations defined by ve…

New constructions in the theory of fields for multiple integrals are designed. Generalizations of the Legendre - Weyl - Caratheodory transforms and corresponding invariant integrals are introduced and explored. Connection and curvature of…

A generalization of the Einstein equation is considered for complex line elements. Several second order semilinear partial differential equations are derived from it as semilinear field equations in uniform and isotropic spaces. The…

Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right hand sides in a global setting. After establishing several…

The methods of classical invariant theory are used to construct generic polynomials for groups $S_5$ and $A_5$, along with explicit reductions to specializations of the generic polynomials defining any desired field extension with those…

We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…

We compare several definitions of the Galois group of a linear difference equation that have arisen in algebra, analysis and model theory and show, that these groups are isomorphic over suitable fields. In addition, we study properties of…

We find the complete set of fundamental invariants for systems of ordinary differential equations of order $\ge 4$ under the group of point transformations generalizing similar results for contact invariants of a single ODE and point…

We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup.…

Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with…

We study invariants under gauge transformations of linear partial differential operators on two variables. Using results of BK-factorization, we construct hierarchy of general invariants for operators of an arbitrary order. Properties of…

Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…

We carry on the approach used in [Sch] to provide a solution for the inverse problem of the calculus of variations for Maxwell equations in vacuum and we provide an abstract theory including all implicit differential equations that can be…

Conformal fields are a new class of $Vect(N)$ modules which are more general than tensor fields. The corresponding diffeomorphism group action is constructed. Conformal fields are thus invariantly defined.

Point transformations for the ordinary differential equations of the form $y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) (y')^2+S(x,y) (y')^3$ are considered. Some classical results are resumed. Solution for the equivalence problem for the equations of…

The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…

The objective of this paper is to analyse analytic invariant sets of analytic ordinary differential equations (ODEs). For this purpose we introduce semi-invariants and invariant ideals as well as the notion of vector fields in Poincare-…

In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.

We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.

We develop a notion of (principal) differential rank for differential-valued fields, in analog of the exponential rank and of the difference rank. We give several characterizations of this rank. We then give a method to define a derivation…

In Tensor Field Theory (TFT), observables are defined through tensor field contractions that produce unitary invariants for complex-valued tensor fields. Traditionally, these observables are constructed using tensor fields of a fixed order…