Abstract
We consider linear differential equations of the second- and the third-order and nonlinear second-order differential equations related via the Schwarzian derivative. The main objective of the paper is to obtain relations between the solutions of the second- and the third-order linear differential equations and the solutions of the nonlinear differential equations of the second order. The method is based on the use of the Schwarzian derivative, which is defined as the ratio of two linearly independent solutions of the linear differential equations of the second and the third order. As a result, we obtain new relations between the solutions of these linear and nonlinear equations.
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Acknowledgements
GF is grateful to the organizers of the conference Modern Mathematical Methods and High Performance Computing in Science and Technology—2018 for their invitation and the opportunity to present a recorded video lecture.
GF also acknowledges the support of the Alexander von Humboldt Foundation and the support of NCN OPUS 2017/25/B/BST1/00931.
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Filipuk, G., Chichurin, A. (2019). The Properties of Certain Linear and Nonlinear Differential Equations. In: Singh, V., Gao, D., Fischer, A. (eds) Advances in Mathematical Methods and High Performance Computing. Advances in Mechanics and Mathematics, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-030-02487-1_11
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DOI: https://doi.org/10.1007/978-3-030-02487-1_11
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