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Symmetries and integration of differential equations
Palabras clave:
Ordinary differential equations, Symmetries, 2000 Mathematics Subject Classification, Primary: 34A26, 54H15, Secondary: 58D19, 35F05 (en)Descargas
Abstract. A proof of the Lie theorem which relates the symmetries of a first order differential equation (or of a linear differential form) with its integrating factors is given. It is shown that a similar result partially applies for systems of linear differential forms and ordinary differential equations of any order.
Referencias
G. F. Simmons, Differential Equations. With Applications and Historical Notes, 2nd ed., 9. McGraw-Hill, New York, 1991.
N. H. Ibragimov, Sophus Lie and Harmony in Mathematical Physics, on the 150th Anniversary of His Birth, The Mathematical Intelligencer 16, 20 (1994).
H. Stephani, Differential Equations: Their Solution Using Symmetries, Cambridge University Press, Cambridge, 1989.
L. Dresner, Applications of Lie’s Theory of Ordinary and Partial Differential Equations, Institute of Physics, Bristol, 1999.
P. E. Hydon, Symmetry Methods for Differential Equations: A Beginner’s Guide, Cambridge University Press, Cambridge, 2000.
C. Von Westenholz, Differential Forms in Mathematical Physics, North-Holland, Amsterdam, 1981.
