Classification of scalar third order ordinary differential equations linearizable via generalized contact transformations

Published in: Quaestiones Mathematicae
Volume 41, issue 1, 2018 , pages: 15–26
DOI: 10.2989/16073606.2017.1369194
Author(s): Hina M. DuttDepartment of Basic Sciences, School of Electrical Engineering and Computer Science, Pakistan, Asghar QadirPhysics Department, School of Natural Sciences, Pakistan
Keywords: 34A30, 34A30


Whereas Lie had linearized scalar second order ordinary differential equations (ODEs) by point transformations, and later Chern had extended to the third order by using contact transformation, till recently no work had been done for higher order (or systems) of ODEs. Lie had found a unique class defined by the number of infinitesimal symmetry generators but the more general ODEs were not so classified. Recently, classifications of higher order and systems of ODEs were provided. In this paper we relate contact symmetries of scalar ODEs with point symmetries of reduced systems. We define a new type of transformation that builds upon this relation and obtain equivalence classes of scalar third order ODEs linearizable via these transformations. Four equivalence classes of such equations are seen to exist.

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