Related papers: Invariants associated with linear ordinary differe…
The method of this paper is my original creation. A new method for solving linear differential equations is proposed in this paper. The important conclusion of this paper is that arbitrary order linear ordinary differential equations with…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
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…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
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.
A systematic group-theoretical analysis of the supersymmetric sinh-Gordon equation is performed. A generalization of the method of prolongations is used to determine the Lie superalgebra of symmetries, and the method of symmetry reduction…
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…
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…
Admissible point transformations of classes of $r$th order linear ordinary differential equations (in particular, the whole class of such equations and its subclasses of equations in the rational form, the Laguerre-Forsyth form, the first…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and show their application to the equivalence problem of such…
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…
Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…
Second order ordinary differential equations that possesses the constant invariant are investigated. Four basic types of these equations were found. For every type the complete list of nonequivalent equations is issued. As the exampes the…
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
A general method for solving linear differential equations of arbitrary order, is used to arrive at new representations for the solutions of the known differential equations, both without and with a source term. A new quasi-solvable…
We find generators for the algebra of rational differential invariants for general and degenerate Kundt spacetimes and relate this to other approaches to the equivalence problem for Lorentzian metrics. Special attention is given to…
We introduce a coarse algebraic invariant for coarse groups and use it to differentiate various coarsifications of the group of integers. This lets us answer two questions posed by Leitner and the second author. The invariant is obtained by…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.