First integrals and reduction of a class of nonlinear higher order ordinary differential equations.
type: Item
instance of: scholarly article
title: First integrals and reduction of a class of nonlinear higher order ordinary differential equations.
zbMATH Open document ID: 1055.34076
DOI: 10.1016/S0022-247X(03)00544-4
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-06T00:00:00Z
review text: This paper is concerned with the resolution of nonlinear higher-order equations of the following form \[ x^{(n)}= h(x, x^{(n-1)}\dot x),\text{ where }\dot x= {dx\over dt}\text{ and }x^{(n)}= {d\over dt} (x^{(n-1)}),\;n\in \mathbb{N}^*. \] The proposed method consists in constructing their first integrals and reducing them. The cases \(n= 3,4\), and \(5\) are discussed in detail and some examples are given.
reviewed by: Mohammed Bouchekif
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 2022070
zbMATH Keywords: nonlinear ordinary differential equations
zbMATH Keywords: first integrals
zbMATH Keywords: Lie point symmetry
author: N. Euler
author: P. G. L. Leach
MaRDI profile type: Publication
cites work: Hidden symmetries associated with the projective group of nonlinear first-order ordinary differential equations
cites work: Complete symmetry groups of ordinary differential equations and their integrals: Some basic considerations
cites work: Q5573571
cites work: Transformation Properties of x'' + f_1(t)x' + f2(t)x + f3(t)x^n = 0
cites work: Linearisable third-order ordinary differential equations and generalised sundman transformations: the case \(X'''=0\)
cites work: Q4236986
cites work: Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry
cites work: On the determination of non-local symmetries
cites work: First integrals for the modified Emden equation q̈+α(t) q̇+q n =0
cites work: Q4036633
cites work: Self-similar solutions of the generalized Emden-Fowler equation
cites work: Symmetries of first integrals and their associated differential equations
cites work: Symmetry, Singularities and Integrability in Complex Dynamics I: The Reduction Problem
cites work: Contact symmetry algebras of scalar second-order ordinary differential equations
cites work: Solution of generalized Emden-Fowler equations with two symmetries
cites work: Q5550465
cites work: Q5550466
cites work: Q5550467
full work available at URL: s0022-247x(03)00544-4
OpenAlex ID: W2088068521
description: scientific article; zbMATH DE number 2022070