Lie group analysis of some new types of integrable differential equations
type: Item
instance of: scholarly article
title: Lie group analysis of some new types of integrable differential equations
zbMATH Open document ID: 0809.58014
author: Qinghua Ma
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-03-29T00:00:00Z
review text: The use of Lie groups is an established way of attempting to solve differential equations. See for instance [\textit{G. Bluman} and \textit{S. Kumei}, ``Symmetries and differential equations'', Springer, New York (1989; Zbl 0698.35001); \textit{P. J. Olver}, ``Applications of Lie groups to differential equations'', Springer, New York (1986; Zbl 0588.22001); \textit{H. Stephani}, ``Differential equations: Their solution using symmetries'', CUP, Cambridge (1989; Zbl 0704.34001)]. Essentially one seeks a point symmetry of the equations being studied and reduces the order or dimensionality by restricting to the invariants of the (local) symmetry group. The present author adds to a literature on second order linear and nonlinear ordinary differential equations studied via this method. He establishes a correspondence between the coefficients in a generic linear equation and those in the infinitesimal symmetry (vector field). By judicious choice of the latter he is then able to describe some integrable classes. This is a rather ad hoc, though traditional, way of proceeding and the results are necessarily of very restricted application.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 35Q58
zbMATH DE Number: 495316
zbMATH Keywords: ordinary differential equation
zbMATH Keywords: Lie groups
zbMATH Keywords: symmetry
zbMATH Keywords: integrable
reviewed by: Christopher Athorne
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1331
OpenAlex ID: W1995959847
Wikidata QID: Q115395438
DOI: 10.1006/JMAA.1993.1331
description: scientific article; zbMATH DE number 495316