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Qadir, Asghar

Linearization: geometric, complex, and conditional. (English) Zbl 1269.34045

J. Appl. Math. 2012, Article ID 303960, 30 p. (2012).
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.

Cited in 3 Documents

MSC:

34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C14 Symmetries, invariants of ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations

Software:

geodesicCOMMENTED.nb
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\textit{A. Qadir}, J. Appl. Math. 2012, Article ID 303960, 30 p. (2012; Zbl 1269.34045)
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References:

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