Related papers: Algebraic method for finding equivalence groups

A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…

Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201…

This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…

In this paper, we propose a numerical method to solve isotropic elliptic equations on point cloud by generalizing the point integral method. The idea of the point integral method is to approximate the differential operators by integral…

We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference…

We perform complete group classification of the general class of quasi linear wave equations in two variables. This class may be seen as a broad generalization of the nonlinear d'Alembert, Liouville, sin/sinh-Gordon and Tzitzeica equations.…

A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using a gauging of…

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…

We identify an interesting special class of prime ideals in the finitary infinite symmetric group algebra. We show that the set of such ideals carries a semiring structure. Over the complex numbers, we establish a connection with spherical…

Totally symmetric sets are a recently introduced tool for studying homomorphisms between groups. In this paper, we give full classifications of totally symmetric sets in certain families of groups and bound their sizes in others. As a…

We use group representation theory to give algebraic formulae to compute complete transversals of singularities of vector fields, either in the nonsymmetric or in the reversible equivariant contexts. This computation produces normal forms…

We complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to…

In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of…

We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…

Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…

We extend the definition of algebraic entropy to semi-discrete (difference-differential) equations. Calculating the entropy for a number of integrable and non integrable systems, we show that its vanishing is a characteristic feature of…

Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…

We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence groupoid of a class of…