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.
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