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In this work, we investigate the long-time asymptotic behavior of theWadati-Konno-Ichikawa equation with initial data belonging to Schwartz space atinfinity by using the nonlinear steepest descent method of Deift and Zhou forthe oscillatory Riemann-Hilbert problem. Based on the initial value condition,the original Riemann-Hilbert problem is constructed to express the solution ofthe Wadati-Konno-Ichikawa equation. Through a series of deformations, theoriginal RH problem is transformed into a model RH problem, from which thelong-time asymptotic solution of the equation is obtained explicitly.

Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data