Canonical variables for one Hamiltonian system (Q1911088)

The authors discuss a system of partial differential equations of the form \(Q^t_1 = [Q_0,M_j]\), \(Q^t_2 = [Q_0,M_{j-1}] + [Q_1,M_j], \dots, Q^t_j= [Q_0,M_1] + \cdots + [Q_{j-1}, M_j]\), with \(M_s= {\delta H \over \delta Q^t_s}\), \(1\leq s \leq j\), where \(Q_1, \dots, Q_j\) are matrices of order \(n\), \(H=H(Q_1, \dots, Q_j)\) and \(Q^t_s\) is the transpose matrix of \(Q_s\). They prove that the above system is Hamiltonian, and obtain Hamiltonian functions \(H\) for which the system possesses a denumerable set of conservation laws.