Related papers: Linearizability Criteria for a Class of Third Orde…
We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm to solve third order difference equations in terms of second order equations, together with applications to…
We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordinary differential equation that admits Bernoulli equation as…
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…
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…
Meleshko presented a new method for reducing third order autonomous ordinary differential equations (ODEs) to Lie linearizable second order ODEs. We extended his work by reducing fourth order autonomous ODEs to second and third order…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
We present here the solution of the problem on linearization of fourth-order equations by means of point transformations. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of…
In this paper, we introduce some analytical techniques to solve some classes of second order differential equations. Such classes of differential equations arise in describing some mathematical problems in Physics and Engineering.
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
Our paper "Solving Third Order Linear Difference Equations in Terms of Second Order Equations" gave two algorithms for solving difference equations in terms of lower order equations: an algorithm for absolute factorization, and an algorithm…
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second order nonlinear ODEs. We show that besides the conventional point, Sundman and generalized…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided. In the particular case of second order linear and nonlinear PDEs and systems of PDEs, necessary and sufficient conditions…
We describe the second order ODE's cubic in the first order derivative with 2-dimensional symmetry algebra. We show that there exist only eight different types of them. We also construct the easily verifiable Equivalence Criterion for every…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
Linearizability is the gold standard among algorithm designers for deducing the correctness of a distributed algorithm using implemented shared objects from the correctness of the corresponding algorithm using atomic versions of the same…