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Classification of Scalar Fourth Order Ordinary Differential Equations Linearizable via Generalized Lie–Bäcklund Transformations

  • Hina M. DuttEmail author
  • Asghar Qadir
Conference paper
  • 418 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 266)

Abstract

Lie had shown that there is a unique class of scalar second order ordinary differential equations (ODEs) that can be converted to linear form by point transformations. Mahomed and Leach had shown that for higher order (than 2) scalar ODEs there are always three classes. Separately, Chern had linearized two classes of third order ODEs by using contact transformations. We provided an (inclusive) classification for third order ODEs by using a generalization of contact transformations. Here we extend that work to the fourth order using a generalization of the Lie–Backlund transformation and demonstrate that there are (at least) four classes of fourth order linearizable ODEs.

Keywords

Generalized Lie–Bäcklund transformations Linearization System of two second order ODEs 

Notes

Acknowledgements

We are grateful to the Higher Education Commission (HEC) of Pakistan for support under their project no. 3054.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Basic Sciences, School of Electrical Engineering and Computer ScienceNational University of Sciences and TechnologyIslamabadPakistan
  2. 2.Physics Department School of Natural SciencesNational University of Sciences and TechnologyIslamabadPakistan

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