Journal of Nonlinear Mathematical Physics

Volume 23, Issue 1, January 2016, Pages 127 - 140

The Elliptic Sinh-Gordon Equation in the Quarter Plane

Authors
Guenbo Hwang
Department of Mathematics, Daegu University, Gyeongsan Gyeongbuk, 712-714, Korea, ghwang@daegu.ac.kr
Received 10 August 2015, Accepted 20 November 2015, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2016.1135646How to use a DOI?
Keywords
Boundary value problem, Integrable system, Sinh-Gordon equation
Abstract

We study the elliptic sinh-Gordon equation formulated in the quarter plane by using the so-called Fokas method, which is a significant extension of the inverse scattering transform for the boundary value problems. The method is based on the simultaneous spectral analysis for both parts of the Lax pair and the global algebraic relation that involves all boundary values. In this paper, we address the existence theorem for the elliptic sinh-Gordon equation posed in the quarter plane under the assumption that the boundary values satisfy the global relation. We also present the formal representation of the solution in terms of the unique solution of the matrix Riemann- Hilbert problem defined by the spectral functions.

Copyright
© 2016 The Authors. Published by Atlantis Press 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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 1
Pages
127 - 140
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2016.1135646How to use a DOI?
Copyright
© 2016 The Authors. Published by Atlantis Press 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

TY  - JOUR
AU  - Guenbo Hwang
PY  - 2021
DA  - 2021/01
TI  - The Elliptic Sinh-Gordon Equation in the Quarter Plane
JO  - Journal of Nonlinear Mathematical Physics
SP  - 127
EP  - 140
VL  - 23
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1135646
DO  - https://doi.org/10.1080/14029251.2016.1135646
ID  - Hwang2021
ER  -