Global solution of the Wadati-Konno-Ichikawa equation with small initial data

Abstract

We show the existence of global solution for the Wadati-Konno-Ichikawa (WKI) equation with small initial data in the smooth function space. Our approach is based on the scattering and inverse scattering maps in the weighted Sobolev spaces for the WKI spectral problem. In addition, we derive one soliton solution as well as a bursting soliton from our matrix Riemann-Hilbert problem.