Applications of tangent transformations to the linearization problem of fourth-order ordinary differential equations

TL;DR

This paper introduces a new set of tangent transformations to extend the linearization methods for fourth-order ordinary differential equations, providing criteria, tests, and explicit procedures for linearization.

Contribution

The paper develops a novel set of tangent transformations that broadens the scope of linearization techniques for fourth-order ODEs, including explicit criteria and procedures.

Findings

Derived criteria for linearizability of fourth-order ODEs

Developed explicit linearization test and transformation procedures

Extended existing transformation sets for broader applicability

Abstract

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. Criteria for fourth-order ordinary differential equations to be linearizable are obtained in a particular case; a linearization test and procedure for obtaining the linearizing transformations are provided in explicit forms.