Hamiltonian structure of Sato's hierarchy of KP equations and a coadjoint orbit of a certain formal Lie group
Results are announced, without proofs, on the Hamiltonian structure of the hierarchy of Kadomtsev-Petviashvili equations introduced by \textit{M. Sato} [Random systems and dynamical systems, Proc. Symp., Kyoto 1981, RIMS Kokyuroku 439, 30-46 (1981; Zbl 0507.58029)]. It is stated that these are completely integrable Hamiltonian systems. The Hamiltonians and conserved densities are given. The underlying symplectic manifold is a Kostant-Kirillov coadjoint orbit, which is described.
completely integrable Hamiltonian systems
scientific article; zbMATH DE number 3936028