Abstract
Hamiltonian operators and their behavior under differential substitutions are studied. Scalar Hamiltonian operators are classified up to fifth order, and it is shown that all such operators may be obtained from the first-order Gardner operator, Dx, by differential substitutions, thus proving an infinite-dimensional Darboux theorem for Hamiltonian systems of evolution equations corresponding to such operators. © 1990 American Institute of Physics. © 2017 Elsevier B.V., All rights reserved.