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2012 Linearization: Geometric, Complex, and Conditional
Asghar Qadir
J. Appl. Math. 2012(SI14): 1-30 (2012). DOI: 10.1155/2012/303960


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.


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Asghar Qadir. "Linearization: Geometric, Complex, and Conditional." J. Appl. Math. 2012 (SI14) 1 - 30, 2012.


Published: 2012
First available in Project Euclid: 16 July 2013

zbMATH: 1269.34045
MathSciNet: MR3005221
Digital Object Identifier: 10.1155/2012/303960

Rights: Copyright © 2012 Hindawi


Vol.2012 • No. SI14 • 2012
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