Symmetry Reductions of Second Heavenly Equation and 2+1-Dimensional Hamiltonian Integrable Systems
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, vol.15, pp.417-425, 2008 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 15
- Publication Date: 2008
- Doi Number: 10.2991/jnmp.2008.15.s3.40
- Journal Name: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.417-425
- Yıldız Technical University Affiliated: Yes
Abstract
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.