Mixed heavenly equation: a new integrable multi-Hamiltonian system

Abstract:
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.