P G L Leach and G P Flessas 2001 J. Phys. A: Math. Gen. 34 6013 doi:10.1088/0305-4470/34/30/312
P G L Leach1 and G P Flessas
Show affiliationsUsing the method of the Lie theory of extended groups and for the parameter values σ = ½, b = 1 and r = 0 we construct explicitly the general exact solution to the real Lorenz equations in terms of Jacobian elliptic functions. In the context of our approach further possible completely integrable cases of the Lorenz system are discussed by considering the result of the Painlevé analysis for σ = 1, b = 2 and r = 1/9 and negative values of r, the latter case, r < 0, for b > 0 and σ > 0 not following from the Painlevé test. For other positive parameter values and in the form of appropriate power series we find some particular exact solutions which do not possess the Painlevé property.
02.20.Qs General properties, structure, and representation of Lie groups
20C33 Representations of finite groups of Lie type
Issue 30 (3 August 2001)
Received 4 August 2000, in final form 29 January 2001
Published 20 July 2001
P G L Leach and G P Flessas 2001 J. Phys. A: Math. Gen. 34 6013
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