The Elliptic Sinh-Gordon Equation in the Quarter Plane
- https://doi.org/10.1080/14029251.2016.1135646How to use a DOI?
- Boundary value problem, Integrable system, Sinh-Gordon equation
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.
- © 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 -