Group Classification of Equations of the Form y″ = f(x,y)
- 45 Downloads
The problem of classification of ordinary differential equations of the form y″ = f(x,y) by admissible local Lie groups of transformations is solved. “Standard” equations are listed on the basis of the equivalence concept. The classes of equations admitting a one‐parameter group and obtained from the “standard” equations by invariant extension are described.
Unable to display preview. Download preview PDF.
- 1.S. Lie, “Classification und integration von gewöhnlichen differential-gleichungen zwischen x, y, die gruppe von transformationen gestatten,” Arch. Math. Natur. Christiania, 9, 371-393 (1883).Google Scholar
- 2.L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York (1982).Google Scholar