Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval. Issue 1 (2nd January 2018)

• Record Type: Journal Article
• Authors: Zhu, Qiaozhen; Xu, Jian; Fan, Engui
• Is Part Of: Journal of nonlinear mathematical physics. Volume 25:Issue 1(2018)
• Page Start: 136
• Page End: 165
• Publication Date: 2018-01-02
• Subjects: Two-component Gerdjikov-Ivanov equation -- initial-boundary value problem -- Fokas unified method -- Riemann-Hilbert problem; Nonlinear theories -- Periodicals; Mathematical physics -- Periodicals; 515.252
• DOI: 10.1080/14029251.2018.1440747
• Languages: English
• ISSNs: 1402-9251

Abstract

Abstract : In this paper, we apply Fokas unified method to study initial-boundary value problems for the two-component Gerdjikov-Ivanov equation formulated on the finite interval with 3×3 Lax pairs. The solution can be expressed in terms of the solution of a 3×3 Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of three matrix-value spectral functions s ( λ ), S ( λ ) and SL ( λ ), which arising from the initial values at t = 0, boundary values at x = 0 and boundary values at x = L, respectively. Moreover, The associated Dirichlet to Neumann map is analyzed via the global relation. The relevant formulae for boundary value problems on the finite interval can reduce to ones on the half-line as the length of the interval tends to infinity.