  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.
