Symmetries, integrals, and three-dimensional reductions of Plebanski's second heavenly equation

Neyzi F., Sheftel M. B. , Yazici D.

PHYSICS OF ATOMIC NUCLEI, vol.70, no.3, pp.584-592, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 3
  • Publication Date: 2007
  • Doi Number: 10.1134/s1063778807030209
  • Title of Journal : PHYSICS OF ATOMIC NUCLEI
  • Page Numbers: pp.584-592


We study symmetries and conservation laws for Plebanski's second heavenly equation written as a first-order nonlinear evolutionary system which admits a multi-Hamiltonian structure. We construct an optimal system of one-dimensional subalgebras and all inequivalent three-dimensional symmetry reductions of the original four-dimensional system. We consider these two-component evolutionary systems in three dimensions as natural candidates for integrable systems.