English

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