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Zakharov, V.E. and Shabat, A. (1972) Exact Theory of Two-Dimensional Self-Focusing and One-Dimensional Self-Modulation of Waves in Nonlinear Media. Soviet Physics, 34, 12-69.

has been cited by the following article:

• 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.