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

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

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