  The problem of linear instability of a nonlinear traveling wave in a
canonical Hamiltonian system with translational symmetry subject to
superharmonic perturbations is discussed. It is shown that exchange of
stability occurs when energy is stationary as a function of wave speed. This
generalizes a result proved by Saffman [3] for traveling wave solutions
exhibiting a wave profile with reflectional symmetry. The present argument
remains true for any noncanonical Hamiltonian system that can be cast in
Darboux form, i.e. a canonical Hamiltonian form on a submanifold defined by
constraints, such as a two-dimensional surface wave on a shearing flow,
revealing a general feature of Hamiltonian dynamics.
