TY - GEN

T1 - Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order

AU - Liu, Yang

AU - Lyakhov, Dmitry

AU - Michels, Dominik L.

N1 - KAUST Repository Item: Exported on 2021-04-14
Acknowledgements: 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.

PY - 2020/10/2

Y1 - 2020/10/2

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/666227

UR - http://link.springer.com/10.1007/978-3-030-60026-6_24

UR - http://www.scopus.com/inward/record.url?scp=85096582974&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-60026-6_24

DO - 10.1007/978-3-030-60026-6_24

M3 - Conference contribution

SN - 9783030600259

SP - 421

EP - 430

BT - Computer Algebra in Scientific Computing

PB - Springer Nature

ER -