  In this paper we found a Lagrangian representation and corresponding
Hamiltonian structure for the constant astigmatism equation. Utilizing this
Hamiltonian structure and extra conservation law densities we construct a first
evolution commuting flow of the third order. Also, we apply the recursion
operator and present a second Hamiltonian structure. This bi-Hamiltonian
structure allows to replicate infinitely many local commuting flows and
corresponding local conservation law densities.
