On group classification of normal systems of linear second-order ordinary differential equations

Abstract

In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results and subsequent Theorem arising from this particular study are discussed here. This paper considers the study of irreducible systems of second-order ordinary differential equations.

Complete group classification of systems of two nonlinear second-Order ordinary differential equations of the form y′′=F(y)Oguis1, Moyo2, Meleshko3 2017Communications in Nonlinear Science and Numerical SimulationSelf Cite1000View full textAdd to dashboardCite

“…As in [22,25] and in the succeeding pages, this transformation places a very important role in the group classification process.…”

“…The latter part of the paper lists the different cases with their respective results and is then followed by the conclusion. This section focuses on systems of two nonlinear second-order ordinary differential equations of the form [22,25] y ′′ = F(x, y),…”

Comment on 'Conformal invariance of the zero-vorticity Lagrangian path in 2D turbulence'

“…6 Equivalence transformations can be successfully applied for example to classify unclosed differential equations according to the number of symmetries they admit when specifying the unclosed terms (see e.g. Meleshko (2002); Khabirov & Ünal (2002a,b); Chirkunov (2012); Meleshko & Moyo (2015); Bihlo & Popovych (2017)). A typical task in this context sometimes is to find a specification of the unclosed terms such that the maximal symmetry algebra is gained.…”

Group Classification and Conservation Laws of a Class of Hyperbolic Equations

“…The group classification of differential equations, which consists in determining all symmetry classes admitted by an equation according to the values of the parameters or arbitrary functions labelling the given family of differential equations, has been carried out in the literature mostly in a more or less ad hoc manner [1][2][3][4][5][6][7]. This has resulted, as pointed out in [7], in a number of revised classification results published in the literature being wrong.…”