Abstract
The long-time asymptotics of the solution of the initial value problem for the potential Wadati-Konno-Ichikawa (pWKI) equation are obtained by using the nonlinear steepest descent method. Based on the spectral analysis and inverse scattering methods, we first construct a basic Riemann-Hilbert problem related to the solution of the pWKI equation. Various Deift-Zhou contour deformations and the motivation behind them are given. Through several proper transformations between the corresponding Riemann-Hilbert problems and strict error estimates, the leading-order asymptotics of the solution of the initial value problem for the pWKI equation is finally obtained.
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