Finding The Lie Symmetries of Some First-Order Odes Via Induced Characteristic

Yıl 2017, Cilt: 13 Sayı: 2, 275 - 278, 30.06.2017

Mehmet Açil , Ali Konuralp , Necdet Bildik

Öz

In this paper,
the first-order ODEs which have no systematic way to find their Lie point
symmetries -unlike higher order ODEs which have systematic ways- are
reconsidered. As a first step, we considered first order PDEs which correspond
to these equations by introducing reduced characteristic Q that used in the
Lie’s theory. Following this step, we tried to obtain solutions of the PDEs
using their Lie point symmetries. But in this process, we met some
difficulties, so by taking into account some assumptions we obtained the
symmetries of ODEs which are in the special form, and also their
solutions. 

Anahtar Kelimeler

Lie point symmetry, Ordinary differential equations, Ricatti differential equations, scale symmetry, prolonged infinitesimals

Kaynakça

• [1] Bildik N.; Açil M. On the Lie Symmetries of First-order Ordinary Differential Equations. AIP Proceeding. 2013; 1558, 2575–2578.
• [2] Hydon P.E. Symmetry Methods for Differential Equations (A Beginner’s Guide). Cambridge Texts in Apllied Mathematics, 2000.
• [3] Cheb-Terrab E.S.; Kolokolnikov T. First-order Ordi-nary Differential Equations. Symmetries and Linear Transformation. European Journal of Applied Mathe-matics. 2003; 14:2 231-246.
• [4] Cheb-Terrab E.S.; Roche A.D. Symmetries and first-order ODE Patterns, Computer Physics Communica-tions. 1998; 113:239-260.
• [5] Andrei D. Polyanin, Valentine F. Zaitsev,Hand Book of Exact Solutions for Ordinary Differential Equations (Second Edition), Chapman - Hall/CRC, 2002.