On the Poisson structure and action–angle variables for the Wadati–Konno–Ichikawa equation

Abstract

In this work, we employ the inverse scattering approach to investigate the Poisson structure and action–angle variables for the Wadati–Konno–Ichikawa equation. The Poisson brackets for the scattering data are deduced. Consequently, the action–angle variables are expressed in terms of the scattering data. In addition, we also discuss on the conservation laws and the spectral parameter expression of Hamiltonian for this equation.