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arXiv · 1709.03881

Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval

Qiaozhen Zhu·Jian Xu·Engui Fan
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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 $3 \times 3$ Lax pairs. The solution can be expressed in terms of the solution of a $3\times3$ Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of three matrix-value spectral functions $s(λ)$, $S(λ)$ and $S_L(λ)$, 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.

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Qiaozhen Zhu, Jian Xu, Engui Fan. 2017-09-09. Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval. https://doi.org/10.1088/0253-6102%2F68%2F4%2F425

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