Using a new definition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theoremsâ€¦ (More)

A D-finite system is a finite set of linear homogeneous partial differential equations in several independent and dependent variables, whose solution space is of finite dimension. Let L be a D-finiteâ€¦ (More)

The theory of transformations for hyperbolic second-order equations in the plane, developed by Darboux, Laplace and Moutard, has many applications in classical differential geometry [12, 13], andâ€¦ (More)

We discuss the problem of exhaustive enumeration of all possible factorization for a given linem ordinary differential operator. A theoretical investigation of topological and combinatorial obstaclesâ€¦ (More)

We classify all integrable 3-dimensional scalar discrete quasilinear equations Q3 = 0 on an elementary cubic cell of the lattice Z 3. An equation Q3 = 0 is called integrable if it may be consistentlyâ€¦ (More)

Using a new deenition of generalized divisors we prove that the lattice of such divisors for a given linear partial differential operator is modular and obtain analogues of the well-known theorems ofâ€¦ (More)

We discuss the problem of manipulation of expressions involving indefinite functions, integration operators and inverses of linear ordinary differential operators (LODO). Using Loewy-Ore formalâ€¦ (More)

We present an algorithm for factoring a zero-dimensional left ideal in the ring <b>Q</b>(<i>x, y</i>) [∂<inf><i>x</i></inf>, ∂<inf><i>y</i></inf>], i.e. factoring a linear homogeneousâ€¦ (More)

was initiated by Dubrovin and Novikov [2] and continued by Mokhov and Ferapontov [5]. In the present paper, we prove a theorem on the existence of three Hamiltonian structures for a diagonalizableâ€¦ (More)

We investigate second order quasilinear equations of the form fijuxixj = 0, where u is a function of n independent variables x1, ..., xn, and the coefficients fij depend on the first orderâ€¦ (More)