Poisson structure and action-angle variables for the Hirota equation

In this work, we employ the inverse scattering transform (IST) to study the action-angle variables for the Hirota equation. Based on variational principle, we demonstrate that an Euler-Lagrange equation is equivalent to the Hirota equation. By using the IST, several properties of scattering data for the equation are discussed, and we calculate their Poisson brackets successfully with the help of tensor product. Interestingly, we reveal that the action-angle variables can be constructed by the scattering data. Furthermore, the spectral parameter expressions of conservation laws for the equation are derived, related to the Hamiltonian formulation for the equation.