Abstract

To the Problem of Contact Symmetries Similarity for Ordinary Differential Equations

M.I.Timoshin (Faculty of Calculus, Samara State Pedagogical University, Samara, Russia)

e-mail: timoshin@ssttu.samara.ru

The correlation of contact transformations and contact symmetries was marked already by S. Lie [1]. The result presented in work [2], allows to investigate the differential equations on the basis of analysis of solvable three-dimensional Lie algebra derived from two point symmetries and one contact symmetry. In the given report the problem of similarity of contact symmetries is considered. The carried out research allows to study the ordinary differential equations on the basis of two-dimensional Lie algebra derived from one point symmetry and one contact symmetry. In the given work the technique of discovery and use of contact symmetries is shown, the illustrative examples are provided. References [1] Hans Stephani ' Differential equations: their solution using symmetries', Cambridge university Press 1989. [2] Timoshin M.I. ' Contact symmetries and finite contact transformation ', Proceedings of the international Conference: Modern group analysis for the new millennium, Ufa 2001.

Section : 12