|
Journal of Lie Theory 34 (2024), No. 1, 093--112 Copyright Heldermann Verlag 2024 σ-Symmetries and First Integral of Differential Equations Xuefeng Zhao College of Mathematics, Jilin University, Changchun, P.R.China zhaoxf20@mails.jlu.edu.cn Yong Li College of Mathematics, Jilin University, Changchun, P.R.China liyong@jlu.edu.cn We provide some geometric properties for σ-symmetries of system of ordinary differential equations. According to the corresponding geometric representation of σ-symmetries and solvable structure, we give the first integrals for the system of first-order ordinary differential equations and for the system of n-order ordinary differential equations which has not enough symmetries and λ-symmetries. Keywords: First integral, Frobenius integrable, sigma-symmetries. MSC: 34A26, 34A34, 34C40. [ Fulltext-pdf (176 KB)] for subscribers only. |