Linearization of third-order ordinary differential equations by point and contact transformations. (English) Zbl 1082.34003

Ibragimov, Nail H.; Meleshko, Sergey V.

J. Math. Anal. Appl. 308, No. 1, 266-289 (2005).

This paper deals with the linearization of the problem \[ y'''= f(x,y,y',y'') \] by means of the point transformations, \(t= \varphi(x,y)\), \(u= \psi(x,y)\) and by mens of contact transformations \(t= \varphi(x,y,p)\), \(u= \psi(x,y,p)\) and \(q= g(x,y,p)\) with \(p= y'\), \(q= u'\). Necessary and sufficient conditions for linearization are presented. Some examples are given.

Reviewer: Pavol Chocholatý (Bratislava)

MSC:

34A25	Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A34	Nonlinear ordinary differential equations and systems
34C20	Transformation and reduction of ordinary differential equations and systems, normal forms

Keywords:

Nonlinear equations; Candidates for linearization; Contact transformations; Relative invariants; Linearization test

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