Modified Hamiltonian systems and canonical transformations arising from the relationship between generalized Zakharov–Shabat and energy-dependent Schrödinger operators

A new family of completely integrable infinite-dimensional Hamiltonian systems is found. Two canonical maps are deduced which transform this family into the families of Hamiltonian systems associated with the generalized Zakharov–Shabat and energy-dependent Schrödinger operators. Through these maps several relevant Hamiltonian structures are connected. In particular, a simple explanation of the second Hamiltonian structure for AKNS equations is given.