Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval. Issue 1 (2nd January 2018) - Zhu, Qiaozhen; Xu, Jian; Fan, Engui
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.