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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:2109.07637 (nlin)
[Submitted on 16 Sep 2021]

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

Authors: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.
Comments: 29 pages, 4 figures
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
Cite as: arXiv:2109.07637 [nlin.SI]
  (or arXiv:2109.07637v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.2109.07637

Submission history

From: Shou-Fu Tian [view email]
[v1] Thu, 16 Sep 2021 00:37:30 UTC (17 KB)
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