---

Journal of Applied Nonlinear Dynamics 3(1) (2014) 27--36 | DOI:10.5890/JAND.2014.03.003

M.I. Timoshin

Ulyanovsk State Technical University, Ulyanovsk, Russian Federation

Download Full Text PDF

 

Abstract

A generalization of S. Lie’s classification of second order ODEs on two-dimensional algebras of point symmetries is constructed. First integrals for found types second order ODEs are reduced. The pos- sibility of the determination of two-dimensional algebras of dynamic symmetries over number field is considered. Interconnection of dy- namic and contact symmetries is demonstrated. On a concrete ex- ample it is shown the procedure of the decomposition of a contact transformation into superposition of point transformation and Leg- endre transformation.

References

1. [1]	Stephani, H. (1989), Differential Equations: Their Solution Using Symmetries, Cambridge university Press.

2. [2]	Timoshin, M.I. (2009), Dynamic symmetries of ODEs, Ufa Mathematical Journal , 1(3), 132–138.

3. [3]	Lie, S. (1891), Vorlesugen uber Differentialgeichungen mit bekannten infinitesimalen TransformationenVorlesugen uber Differentialgeichungen mit bekannten infinitesimalen Transformationen, Leipzig: B.G. Teubner.

4. [4]	Timoshin, M.I. (2009), Dynamic symmetries of ODEs, Ufa Mathematical Journal , 1(3), 132–138.

5. [5]	Goursat, E. (1917), Cours D’analyse mathematique, Gauthier-Villars, Paris, tome 2, part 2.

6. [6]	Ibragimov, N.H. (1985), Transformation Groups Applied to Mathematical Physics, Dorbrecht, Reidel.

7. [7]	Timoshin, M.I. (2001), Contact symmetries and finite contact transformation, Repots present at international conference ”Mogran” USATU, Ufa Mathematical Journal, 140–143.

8. [8]	Timoshin, M.I. (2002), To the Problem of Contact Symmetries Similarity for Ordinary Differential Equations, Reports present at 16 international Symposium on Nonlinear Acoustics Moscow State University , 1, 611–614.

9. [9]	Klein, F. (1926), Vorlesungen uber Hohere Geometrie, Verlag Van Julius Springer, Berlin.