论文信息 - Complete symmetry groups of ordinary differential equations and their integrals : Some basic considerations

Complete symmetry groups of ordinary differential equations and their integrals : Some basic considerations

Abstract The concept of the complete symmetry group of a differential equation introduced by J. Krause (1994, J. Math. Phys. 35 , 5734–5748) is extended to integrals of such equations. This paper is devoted to some aspects characterising complete symmetry groups. The algebras of the symmetries of both differential equations and integrals are studied in the context of equations for which the elements are represented by point or contact symmetries so that there is no ambiguity about the group. Both algebras and groups are found to be nonunique.

[1] P. Leach. Generalized Ermakov systems , 1991 .

[2] B. Abraham-Shrauner,et al. HIDDEN AND CONTACT SYMMETRIES OF ORDINARY DIFFERENTIAL EQUATIONS , 1995 .

[3] F. Mahomed,et al. THE LINEAR SYMTRIES OF A NONLINEAR DIFFERENTIAL EQUATION , 1985 .

[4] K. Govinder,et al. Characterisation of the Algebraic Properties of First Integrals of Scalar Ordinary Differential Equations of Maximal Symmetry , 1997 .

[5] Fazal M. Mahomed,et al. Symmetry Lie algebras of nth order ordinary differential equations , 1990 .

[6] Edmund Pinney,et al. The nonlinear differential equation ”+()+⁻³=0 , 1950 .

[7] E. Kamke. Differentialgleichungen. Losungsmethoden und Losungen. I , 1952 .

[8] J. Krause,et al. On the complete symmetry group of the classical Kepler system , 1994 .

[9] K. Govinder,et al. The Algebraic Structure of the First Integrals of Third-Order Linear Equations , 1995 .

[10] F. Mahomed,et al. Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra , 1988 .

[11] Maria Clara Nucci,et al. The complete Kepler group can be derived by Lie group analysis , 1996 .