Symmetry in Nonlinear Mathematical Physics - 2009

Devrim Yazici (Yildiz Technical University, Istanbul, Turkey)
Mikhail B. Sheftel (Bogazici University, Istanbul, Turkey & North Western State Technical University, St. Petersburg, Russia)

Mixed heavenly equation: a new integrable multi-Hamiltonian system

In the recent paper by one of the authors (MBS) and A.A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries , mixed heavenly equation appears as one of the canonical equations admitting partner symmetries. Here for the mixed heavenly equation, formulated in a two-component form, we present a Lax pair of Olver&8211;Ibragimov–Shabat type and obtain its multi-Hamiltonian structure. Thus, we discover a new integrable Hamiltonian system.