Symmetry reduction of the first heavenly equation and 2

Creative Commons License

YAZICI D.

TURKISH JOURNAL OF PHYSICS, vol.42, no.2, pp.183-190, 2018 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.3906/fiz-1710-5
  • Journal Name: TURKISH JOURNAL OF PHYSICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.183-190
  • Keywords: First heavenly equation, symmetry reduction, recursion operator, bi-Hamiltonian, 2 + 1-dimensional systems
  • Yıldız Technical University Affiliated: Yes

Abstract

The first heavenly equation of Plebanski in the two-component form is known to be a 3 + 1-dimensional tri-Hamiltonian system. We show that a particular choice of symmetry reduction applied to the first heavenly equation yields a 2+1-dimensional bi-Hamiltonian system. For this tri-dimensional system, we present Lagrangian, Hamiltonian, and recursion operators; point symmetries; and integrals of motions.