Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order

  • Yang Liu
  • Dmitry LyakhovEmail author
  • Dominik L. Michels
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12291)


We consider the problem of the exact linearization of scalar nonlinear ordinary differential equations by contact transformations. This contribution is extending the previous work by Lyakhov, Gerdt, and Michels addressing linearizability by means of point transformations. We have restricted ourselves to quasi-linear equations solved for the highest derivative with a rational dependence on the occurring variables. As in the case of point transformations, our algorithm is based on simple operations on Lie algebras such as computing the derived algebra and the dimension of the symmetry algebra. The linearization test is an efficient algorithmic procedure while finding the linearization transformation requires the computation of at least one solution of the corresponding system of the Bluman-Kumei equation.


Contact symmetry Differential Thomas decomposition Exact linearization Nonlinear ordinary differential equations Symbolic computation 



This work has been funded by the King Abdullah University of Science and Technology (KAUST baseline funding). The authors are grateful to Peter Olver for helpful discussions and to the anonymous reviewers for comments that led to improvement of the paper.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Visual Computing CenterKing Abdullah University of Science and TechnologyThuwalKingdom of Saudi Arabia

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