Linearization: geometric, complex, and conditional
type: Item
instance of: scholarly article
title: Linearization: geometric, complex, and conditional
zbMATH Open document ID: 1269.34045
DOI: 10.1155/2012/303960
author: Asghar Qadir
published in: Journal of Applied Mathematics
publication date: 2013-06-03T00:00:00Z
review text: Summary: Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of) differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it), and then more recent developments based on geometry and complex analysis, apart from Lie's own method of algebra (namely, Lie group theory), are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 34A05
zbMATH DE Number: 6169886
Wikidata QID: Q58906599
describes a project that uses: geodesicCOMMENTED.nb
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/303960
OpenAlex ID: W2138941560
cites work: Q5625579
cites work: Q5765686
cites work: Q5778472
cites work: The characterization of third order ordinary differential equations admitting a transitive fiber-preserving point symmetry group
cites work: Symmetry Lie algebras of \(n\)th order ordinary differential equations
cites work: The geometry of the equation \(y'''=f(x,y,y',y'')\)
cites work: Linearization of third-order ordinary differential equations by point and contact transformations
cites work: Linearization of fourth-order ordinary differential equations by point transformations
cites work: Lie point symmetries for systems of second order linear ordinary differential equations
cites work: Symmetry breaking for a system of two linear second-order ordinary differential equations
cites work: Linearization criteria for a system of second-order ordinary differential equations
cites work: Q3593834
cites work: Projective geometry of systems of second-order differential equations
cites work: The connection between isometries and symmetries of geodesic equations of the underlying spaces
cites work: Linearization criteria for a system of second-order quadratically semi-linear ordinary differential equations
cites work: Invariant Linearization Criteria for Systems of Cubically Nonlinear Second-Order Ordinary Differential Equations
cites work: Linearization criteria for a system of two second-order ordinary differential equations
cites work: On the complete integrability and linearization of nonlinear ordinary differential equations. V. Linearization of coupled second-order equations
cites work: A Systematic Method of Finding Linearizing Transformations for Nonlinear Ordinary Differential Equations I: Scalar Case
cites work: Complex Lie symmetries for scalar second-order ordinary differential equations
cites work: Q3557982
cites work: Symmetry group classification of ordinary differential equations: Survey of some results
cites work: On linearization of third-order ordinary differential equations
cites work: Another representation for the maximal Lie algebra of \(\mathfrak{sl}(n+2,\mathbb R)\) in terms of operators
cites work: Symmetries of differential equations. IV
cites work: Constructing a space from the geodesic equations
cites work: A prescription for \(n\)-dimensional Vierbeins
cites work: Linearizability criteria for systems of two second-order differential equations by complex methods
cites work: Lie and Noether symmetries of geodesic equations and collineations
cites work: Faster than Hermitian Quantum Mechanics
cites work: Complex trajectories of a simple pendulum
cites work: Complexified dynamical systems
cites work: Quantum effects in classical systems having complex energy
cites work: Q5455323
cites work: Interactions of Hermitian and non-Hermitian Hamiltonians
cites work: Complex Lie Symmetries for Variational Problems
cites work: Algebraic linearization criteria for systems of ordinary differential equations
cites work: Characterization of the Newtonian free particle system in \(m\geqslant 2\) dependent variables
cites work: Inequivalence of classes of linearizable systems of second order ordinary differential equations obtained by real and complex symmetry analysis
cites work: Conditional linearizability criteria for a system of third-order ordinary differential equations
cites work: Conditional Linearizability of Fourth-Order Semi-Linear Ordinary Differential Equations
cites work: Classification of ordinary differential equations by conditional linearizability and symmetry
description: scientific article; zbMATH DE number 6169886