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

Abstract

Admissible point transformations of classes of $r$th 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 revisited within the algebraic approach in three different ways.

22 pages, essentially revised and extended version

References in corpus (4)

• Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
• Conservation Laws and Potential Symmetries of Linear Parabolic Equations
• Equivalence transformations in the study of integrability
• Application of Group Analysis to Classification of Systems of Three Second-Order Ordinary Differential Equations

Cited by in corpus (7)

• Group classification of linear evolution equations
• Group analysis of general Burgers-Korteweg-de Vries equations
• Equivalence groupoid of a class of variable coefficient Korteweg--de Vries equations
• Equivalence groupoid and group classification of a class of variable-coefficient Burgers equations
• Realizations of Lie algebras on the line and the new group classification of (1+1)-dimensional generalized nonlinear Klein-Gordon equations
• Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations
• Lie reductions and exact solutions of dispersionless Nizhnik equation