Symmetries, integrals and solutions of ordinary differential equations of maximal symmetry
The authors review the properties of the standard symmetries of the representative equations of the second- and third-order of maximal symmetry of point (second-order) and contact (third-order) symmetries in terms of the corresponding finite transformations and actions on solutions and fundamental first integrals. In the case of so-called exceptional symmetries (i.e. those not considered to be generic to scalar equations of maximal symmetry) it is shown how to construct an equivalence class with a property as coherent as found for the other classes of symmetry. Some properties of these symmetries are demonstrated.
scientific article; zbMATH DE number 5703365
scientific article