Equivalence groupoids of classes of linear ordinary differential equations and their group classification

7th International Workshop: Group Analysis of Differential Equations and Integrable Systems

Boyko, Vyacheslav M.^1 ; Popovych, Roman O.^1,2 ; Shapoval, Nataliya M.^3

Institute of Mathematics, NAS of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4

01601, Ukraine^1

Wolfgang Pauli Institut, Universität Wien, Oskar-Morgenstern-Platz 1, Wien

A-1090, Austria^2

Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, 4e Academician Glushkov Ave., Kyiv

03127, Ukraine^3

关键词: Algebraic approaches;    Group classification;    Laguerre;    Linear ordinary differential equations;    Point transformations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/621/1/012002/pdf
DOI  :  10.1088/1742-6596/621/1/012002

来源: IOP

【 摘 要 】

Admissible point transformations of classes of rth order linear ordinary differential equations (in particular, the whole class of such equations and its subclasses of equations in the rational form, the Laguerre-Forsyth form, the first and second Arnold forms) are exhaustively described. Using these results, the group classification of such equations is carried out within the algebraic approach in three different ways.