𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Exceptional Properties of Second and Third Order Ordinary Differential Equations of Maximal Symmetry

✍ Scribed by S Moyo; P.G.L Leach

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
137 KB
Volume
252
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

The Riccati transformation is used in the reduction of order of second and third Ε½ . order ordinary differential equations of maximal symmetry. The sl 2, R subalgebra is preserved under this transformation. The Riccati transformation is itself associated with the symmetry that is annihilated in the reduction of order. The solution symmetries and the intrinsically contact symmetries become nonlocal symmetries under the Riccati transformation. We investigate the fate and origins of the contact symmetries arising from the Riccati transformation. The exceptional properties of the second and third order equations of maximal symmetry are indicated. In the context of generalised symmetries we express the solution symmetries, Ε½ . contact symmetries, and the sl 2, R elements in terms of a Jacobian. We show that a basis for the solution set of equations of maximal symmetry is given in terms of the solution set of a second order ordinary differential equation.

πŸ“œ SIMILAR VOLUMES

Symmetries of first-order stochastic ord
Symmetries of first-order stochastic ordinary differential equations revisited
✍ E. Fredericks; F. M. Mahomed πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 136 KB

## Abstract Symmetries of stochastic ordinary differential equations (SODEs) are analysed. This work focuses on maintaining the properties of the Weiner processes after the application of infinitesimal transformations. The determining equations (DEs) for first‐order SODEs are derived in an ItΓ΄ calc

Characterisation of the Algebraic Proper
Characterisation of the Algebraic Properties of First Integrals of Scalar Ordinary Differential Equations of Maximal Symmetry
✍ G.P Flessas; K.S Govinder; P.G.L Leach πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 233 KB

We undertake a study of the first integrals of linear nth order scalar ordinary differential equations with maximal symmetry. We establish patterns for the first integrals associated with these equations. It is shown that second and third order equations are the pathological cases in the study of hi

The Characterization of Third Order Ordi
The Characterization of Third Order Ordinary Differential Equations Admitting a Transitive Fiber-Preserving Point Symmetry Group
✍ Guy Grebot πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 211 KB

Third order ordinary differential equations admitting a transitive symmetry group of fiber-preserving point transformations are completely characterized. We give the general expressions of these equations, as well as the canonical equations representing the equivalence classes. The symmetry groups a

Interval Criteria for Oscillation of Sec
Interval Criteria for Oscillation of Second-Order Linear Ordinary Differential Equations
✍ Q. Kong πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 92 KB

Ε½ X . X New oscillation criteria are established for the equation py q qy s 0 that are different from most known ones in the sense that they are based on the informaw . tion only on a sequence of subintervals of t , Ο± , rather than on the whole 0 half-line. Our results are more natural according to