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Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a…

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…

Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…

Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…

Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between $\lambda$-symmetries and first integrals. This relation further leads to a new $\lambda$-symmetry linearization…

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…

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…

The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…

Here we give a complete group classification of the general case of linear systems of three second-order ordinary differential equations excluding the case of systems which are studied in the literature. This is given as the initial step in…

The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…

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…

The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…

In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear…

A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…

In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations. Its ODEs…

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…

Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…