Symmetries, integrals and hierarchies of new (3+1)-dimensional bi-Hamiltonian systems of Monge-Ampere type

JOURNAL OF GEOMETRY AND PHYSICS

卷:146

Article

Sheftel, M. B.¹  Yazici, D.² 

[1] Bogazici Univ, Dept Phys, TR-34342 Istanbul, Turkey

[2] Yildiz Tech Univ, Dept Phys, TR-34220 Istanbul, Turkey

关键词: Monge-Ampere equations;    Point symmetries;    Conserved densities;    Recursion operator;    Hamiltonian operator;    bi-Hamiltonian hierarchy;   

DOI  :  10.1016/j.geomphys.2019.103513

来源: Elsevier

【 摘 要 】

We study point symmetries, the corresponding conserved densities and hierarchies of four new bi-Hamiltonian heavenly systems in 3 + 1 dimensions which we discovered recently. We exhibit an important role played by the inverse recursion operators in the description of the hierarchies. Their use is twofold, either to provide the correct bi-Hamiltonian representation or to generate nonlocal symmetry flows. Invariant solutions w.r.t. nonlocal symmetries will generate (anti-)self-dual gravitational metrics which do not admit Killing vectors which is a characteristic feature of K3 gravitational instanton. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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