On the Poisson structure and action-angle variables for the Fokas-Lenells equation

In this paper, we employ the inverse scattering transform to investigate the action-angle variables of the Fokas-Lenells equation. Firstly, the Fokas-Lenells equation is derived by the variational principle, and the definition of the Poisson structure is presented. Then, the Poisson brackets between the scattering data are successfully determined by introducing the matriz tensor product. Thus the action-angle variables can be constructed by scattering data. Furthermore, the Hamiltonian of the Fokas-Lenells equation in terms of the scattering data is presented, and the Hamiltonian formalism of the equation is derived. (c) 2024 Elsevier B.V. All rights reserved.