Lagrangian and Hamiltonian structures for the constant astigmatism equation

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. We also apply the recursion operator and present a second Hamiltonian structure. This bi-Hamiltonian structure allows us to replicate infinitely many local commuting flows and corresponding local conservation law densities.