Journal of Nonlinear Mathematical Physics

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Volume 25, Issue 1, February 2018, Pages 136 - 165

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

Authors
Qiaozhen Zhu, Jian Xu, Engui Fan*
School of Mathematical Sciences, Fudan University, NO.220 Handan Road, Shanghai, 200433, People’s Republic of China,qiaozhenzhu13@fudan.edu.cn
College of Science, University of Shanghai for Science and Technology, NO.334 Jungong Road, Shanghai 200093, People’s Republic of China,jianxu@usst.edu.cn
School of Mathematical Sciences, Fudan University, NO.220 Handan Road, Shanghai, 200433, People’s Republic of China,faneg@fudan.edu.cn
*Corresponding author.
Corresponding Author
Engui Fan
Received 12 October 2017, Accepted 28 October 2017, Available Online 6 January 2021.
DOI
10.1080/14029251.2018.1440747How to use a DOI?
Keywords
Two-component Gerdjikov-Ivanov equation; initial-boundary value problem; Fokas unified method; Riemann-Hilbert problem
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.

Copyright
© 2018 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
25 - 1
Pages
136 - 165
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2018.1440747How to use a DOI?
Copyright
© 2018 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Qiaozhen Zhu
AU  - Jian Xu
AU  - Engui Fan
PY  - 2021
DA  - 2021/01/06
TI  - Initial-boundary value problem for the two-component Gerdjikov-Ivanov equation on the interval
JO  - Journal of Nonlinear Mathematical Physics
SP  - 136
EP  - 165
VL  - 25
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2018.1440747
DO  - 10.1080/14029251.2018.1440747
ID  - Zhu2021
ER  -