Nonlocal symmetries and integrable ordinary differential equations: xuml+3xx center dot+x(3)=0 and its generalizations


KARASU A. , Leach P. G. L.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.50, 2009 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 50 Konu: 7
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1063/1.3158856
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS

Özet

The equation xuml+3xx center dot+x(3)=0 is well known in many areas of mathematics and physics. It possesses the algebra sl(3,R) of Lie point symmetries, hence is equivalent to the equation for a free particle, and both left and right Painleveacute series. We investigate two higher-dimensional analogs in terms of their symmetry and singularity structures. We find a drastic reduction in symmetry and a loss of some of the singularity properties. From the nonlocal symmetries we are able to determine the complete symmetry group as being represented by a five-dimensional Abelian algebra.