A Relationship between the Ablowitz-Kaup-Newell-Segur and Wadati-Konno-Ichikawa Schemes of the Inverse Scattering Method

Abstract

It is shown that two inverse scattering formalisms by Ablowitz, Kaup, Newell and Segur and by Wadati, Konno and Ichikawa are connected through a gauge tranformation and a transformation of the space and time coordinates depending on a dependent variable. One-soliton solutions of equations associated with the W-K-I scheme are also examined.