Self-dual gravity is completely integrable
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, cilt.41, sa.39, 2008 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 41 Sayı: 39
- Basım Tarihi: 2008
- Doi Numarası: 10.1088/1751-8113/41/39/395206
- Dergi Adı: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
We discover a multi-Hamiltonian structure of a complex Monge-Ampere equation (CMA) set in a real first-order 2-component form. Therefore, by Magri's theorem this is a completely integrable system in four real dimensions. We start with Lagrangian and Hamiltonian densities and obtain a symplectic form and the Hamiltonian operator that determines the Dirac bracket. We have calculated all point symmetries of the 2-component CMA system and Hamiltonians of the symmetry flows. We have found two new real recursion operators for symmetries which commute with the operator of a symmetry condition on solutions of the CMA system. These operators form two Lax pairs for the 2-component system. The recursion operators, applied to the first Hamiltonian operator, generate infinitely many real Hamiltonian structures. We show how to construct an infinite hierarchy of higher commuting flows together with the corresponding infinite chain of their Hamiltonians.