2016/06/26 by J. C. Ndogmo, Ndogmo, J. C.
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic structure #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Lie symmetry algebras #Maximal dimensions #Nonlinear Waves and Solitons #Systems of ordinary differential equations
paper · pdf · doi:10.48550/arxiv.1606.08074
openalex publication_date 2016/06/26 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/28
It is known for scalar ordinary differential equations, and for systems of ordinary differential equations of order not higher than the third, that their Lie point symmetry algebras is of maximal dimension if and only if they can be reduced by a point transformation to the trivial equation y(n)=0. For arbitrary systems of ordinary differential equations of order n ≥ 3 reducible by point transformations to the trivial equation, we determine the complete structure of their Lie point symmetry algebras as well as that for their variational, and their divergence symmetry algebras. As a corollary, we obtain the maximal dimension of the Lie point symmetry algebra for any system of linear or nonlinear ordinary differential equations.