TITLE:
Multi-Cuspon Solutions of the Wadati-Konno-Ichikawa Equation by Riemann-Hilbert Problem Method
AUTHORS:
Youzhi Tu
KEYWORDS:
WKI Equation, Initial Value Problem, Cuspon Solution, Riemann-Hilbert Problem
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.10 No.3,
March
19,
2020
ABSTRACT: In this paper, we consider the initial value problem for a complete
integrable equation introduced by Wadati-Konno-Ichikawa (WKI). The solution
is
reconstructed in terms of the solution of a
matrix Riemann-Hilbert problem via the asymptotic behavior of the spectral variable at
one non-singularity point, i.e.,
. Then, the one-cuspon solution, two-cuspon solutions and
three-cuspon solution are discussed in detail. Further, the numerical simulations
are given to show the dynamic behaviors of these soliton solutions.