Symmetry Reductions of Second Heavenly Equation and 2+1-Dimensional Hamiltonian Integrable Systems


YAZICI D. , Sheftel M. B.

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, cilt.15, ss.417-425, 2008 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 15
  • Basım Tarihi: 2008
  • Doi Numarası: 10.2991/jnmp.2008.15.s3.40
  • Dergi Adı: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
  • Sayfa Sayısı: ss.417-425

Özet

Second heavenly equation of Plebanski, presented in a two-component form, is known to be a 3+ 1-dimensional multi-Hamiltonian integrable system. We show that one symmetry reduction of this equation yields a two component 2+ 1 -dimensionalmulti-Hamiltonian integrable system. For this system, we present Hamiltonian and recursion operators, point symmetries and integrals of motion. For another symmetry reduction, the reduced system is "almost bi-Hamiltonian", with two known Hamiltonian operators but the second Hamiltonian density missing.