Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data
Exactly Solvable and Integrable Systems
2021-09-17 v1 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.2109.07637,
title = {Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data},
author = {Xin Wu and Shou-Fu Tian},
journal= {arXiv preprint arXiv:2109.07637},
year = {2021}
}
Comments
29 pages, 4 figures