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arXiv · 2109.07637

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

Xin Wu·Shou-Fu Tian
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Abstract

In this work, we investigate the long-time asymptotic behavior of the Wadati-Konno-Ichikawa equation with initial data belonging to Schwartz space at infinity by using the nonlinear steepest descent method of Deift and Zhou for the oscillatory Riemann-Hilbert 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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Xin Wu, Shou-Fu Tian. 2021-09-16. Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data. https://arxiv.org/abs/2109.07637

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