Sundman Symmetries of Nonlinear Second-Order and Third-Order Ordinary Differential Equations
β Scribed by Euler, Norbert; Euler, Marianna
- Book ID
- 126745313
- Publisher
- Atlantis Press
- Year
- 2004
- Tongue
- English
- Weight
- 203 KB
- Volume
- 11
- Category
- Article
- ISSN
- 1402-9251
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
Necessary and sufficient conditions which allow the most general third-order ordinary differential equation x 000 ΒΌ f Γ°t; x; x 0 ; x 00 Γ to be transformed to X 000 ΓΎ aX ΒΌ 0 under the generalized Sundman transformation X ΒΌ FΓ°t; xΓ; dT ΒΌ GΓ°t; xΓdt; Γ°F x G -0Γ; are obtained in the paper. Here a -0 is
A scalar complex ordinary differential equation can be considered as two coupled real partial differential equations, along with the constraint of the Cauchy-Riemann equations, which constitute a system of four equations for two unknown real functions of two real variables. It is shown that the resu