Related papers: Integral equivalence of multidimensional different…
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…
The conditions of cylindricality and autonomy of first integrals, last multipliers and integral manifolds for linear homogeneous systems of partial differential equations and total differential systems are established.
In the framework of bidifferential graded algebras, we present universal solution generating techniques for a wide class of integrable systems.
The Integration Theory of Linear Ordinary Differential Equation.
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
An approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented. It provides a truly infinite dimensional construction of integrals as linear…
Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are…
We consider the generalization of Laplace invariants to linear differential systems of arbitrary rank and dimension. We discuss completeness of certain subsets of invariants.
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…
The spectral method for building first integrals of ordinary linear differential systems is elaborated. Using this method, we obtain bases of first integrals for linear differential systems with constant coefficients, for linear…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
We prove an effective integrability criterion for differential-algebraic Pfaffian systems leading to a decision method of consistency with a triple exponential complexity bound. As a byproduct, we obtain an upper bound for the order of…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.