An elementary demonstration of the existence of sℓ(3, R) symmetry for all second-order linear ordinary differential equations

SIAM Review

Volumn 40, Issue 4, 1998, Pages 945-946

  Govinder, K S ^a   Leach, P G L ^a  

^a UNIVERSITY OF KWAZULU NATAL   (South Africa)

Author keywords

Linear differential equations; s (3, R)

Indexed keywords

ALGEBRA; LINEAR ALGEBRA; LINEAR EQUATIONS;

LINEAR DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 0032288343     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144597316838     Document Type: Article

References (8)

1. M. AGUIRRE AND J. KRAUSE, SL(3, K) as the group of symmetry transformations for all onedimensional linear systems, J. Math. Phys., 29 (1988), pp. 9-15.
2. R. L. ANDERSON AND S. M. DAVISON, A generalization of Lie's "counting" theorem for secondorder ordinary differential equations, J. Math. Anal. Appl., 48 (1974), pp. 301-315.
3. E. L. INCE, Ordinary Differential Equations, Longmans, Green and Co., London, 1927.
4. L. M. BERKOVIĆ, Glyden-Meščerskii problem, Celest. Mech., 24 (1981), pp. 407-429.
5. F. M. MAHOMED, Classification of Nonlinear Ordinary Differential Equations According to Their Symmetries, Ph.D. thesis, University of the Witwatersrand, Johannesburg, 1986.
6. F. M. MAHOMED AND P. G. L. LEACH, The Lie algebra sℓ(3, R) and linearization, Quæst. Math., 12 (1989), pp. 121-139.
7. F. M. MAHOMED AND P. G. L. LEACH, Symmetry Lie algebras of nth order ordinary differential equations, J. Math. Anal. Appl., 151 (1990), pp. 80-107.
8. C. E. WULFMAN AND B. G. WYBOURNE, The Lie group of Newton's and Lagrange's equations for the harmonic oscillator, J. Phys. A, 9 (1976), pp. 507-518.