Lagrangian and Hamiltonian structures for the constant astigmatism equation

Maxim V Pavlov, Sergej A Zykov
2013 Journal of Physics A: Mathematical and Theoretical  
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.
doi:10.1088/1751-8113/46/39/395203 fatcat:bhbcz7jo7baxfd4t3ngvxwai2y