On B u -Hamiltonian equations in mechanics of infinite-dimensional systems

Bu-Hamiltonian equations in mechanics of infinite-dimensional systems are studied. The equation of motion represented in the operator form is considered. A linear operator is called Bu-Hamiltonian with respect to the bilinear form if there exists an operator. The representability of this operator equation in the form of a Bu-Hamiltonian equation is studied. The representability of an equation depending on linear operator in the form of a B-Hamiltonian equation is also studied.