相关论文: On First Order Symmetry Operators for the Field Eq…

We determine the general form of the first order linear symmetry operators for the linearized field equation of metric perturbations in the spacetimes of dimension D>=4. Apart from the part derived easily from the invariance under general…

The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…

The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…

We study the ladder operator on scalar fields, mapping a solution of the Klein-Gordon equation onto another solution with a different mass, when the operator is at most first order in derivatives. Imposing the commutation relation between…

We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation…

We present a general procedure to solve the equations of motion for cosmological models driven by real scalar fields with first-order differential equations. The method seems to have great power, since it works for closed, flat or open…

An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a…

The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations,…

Given holomorphic functions $\psi_0$ and $\psi_1$, we consider first-order differential operators acting on Hardy space, generated by the formal differential expression $E(\psi_0,\psi_1)f(z)=\psi_0(z)f(z)+\psi_1(z)f'(z)$. We characterize…

The reduction operators, i.e., the operators of nonclassical (conditional) symmetry, of (1+1)-dimensional second order linear parabolic partial differential equations and all the possible reductions of these equations to ordinary…

The problem of equivalency for linear differential operators of the first order is discussed.

In this paper we extend our recent results (hep-th/0304067) on the first order formulation for the massless mixed symmetry tensor fields to the case of massive fields both in Minkowski as well as in (Anti) de Sitter spaces (including all…

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the $N$-dimensional unit ball $\mathbb{B}^N$ and $\mathbb{D}^2$ of $2\times2$ complex matrices satisfying $I-ZZ^*>0$.Our main tools are the discrete…

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian…

The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…

Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of…

Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic…

We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…

We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…