A simple way of making a Hamiltonian system into biHamiltonian one

Given a Hamiltonian structure $P_0$, we present a set of easily verifiable necessary and sufficient conditions for the existence of Hamiltonian structures compatible with $P_0$, and use these results for the construction of completely integrable biHamiltonian systems.

Keywords. Compatible Hamiltonian structures, biHamiltonian systems, integrability, Poisson bivector, Schouten bracket, master symmetry.

MS 2000 Classification. Primary: 37K10; Secondary: 37K05, 37J35.