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Geometric Linearization of Ordinary Differential Equations
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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Geometric Linearization of Ordinary Differential Equations
Інший ID:
2000 Mathematics Subject Classification: 34A34; 34A26
Посилання:
Geometric Linearization of Ordinary Differential Equations / A. Qadir // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 21 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). I am grateful to NUST for travel support and to the organizers of the Symmetry-2007 and the International Mathematical Union for local support and hospitality at the conference where this paper was presented. I am also grateful for useful comments to Professors Leach, Mahomed, Meleshko and Popovych. Thanks also to DECMA and CAM of the of Wits University, Johannesburg, South Africa for support at the University where the paper was completed.
Дата:
2007
Переглядів:
554
Завантажень:
257
Анотація:
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable equations and even on systems of equations. However, little has been done in the way of providing explicit criteria to determine their linearizability. Using the connection between isometries and symmetries of the system of geodesic equations criteria were established for second order quadratically and cubically semi-linear equations and for systems of equations. The connection was proved for maximally symmetric spaces and a conjecture was put forward for other cases. Here the criteria are briefly reviewed and the conjecture is proved.
