Bi-Hamiltonian structure of the general heavenly equation

24th International Conference on Integrable Systems and Quantum symmetries

Sheftel, M.B.^1 ; Malykh, A.A.^2 ; Yazici, D.^3

Department of Physics, Boazici University, Bebek, Istanbul

34342, Turkey^1

Department of Numerical Modeling, Russian State Hydrometeorlogical University, Malookhtinsky prospect 98, St. Petersburg

195196, Russia^2

Department of Physics, Yildiz Technical University, Esenler, Istanbul

34220, Turkey^3

关键词: Bi-hamiltonian structures;    Hamiltonian operators;    Hamiltonian structures;    Hamiltonian systems;    Lagrangian;    Lax pairs;    Recursion operators;    Two-component;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/804/1/012039/pdf
DOI  :  10.1088/1742-6596/804/1/012039

来源: IOP

【 摘 要 】

We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equation to a two-component form, we obtain Lagrangian and Hamiltonian structures of the two-component general heavenly system. We discover that in the twocomponent form we have only a single nonlocal recursion operator. Composing the recursion operator with the first Hamiltonian operator we obtain second Hamiltonian operator. Thus, the general heavenly equation in the two-component form is a bi-Hamiltonian system completely integrable in the sense of Magri.