The elliptic sinh-Gordon equation in a semi-strip

Advances in Nonlinear Analysis

article

Guenbo Hwang¹ 

[1] Department of Mathematics, Daegu University

关键词: Boundary value problems;    elliptic PDEs;    sinh-Gordon equation;    integrable equations;   

DOI  :  10.1515/anona-2016-0206

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

We study the elliptic sinh-Gordon equation posed in a semi-strip by applying the so-called Fokas method, a generalization of the inverse scattering transform for boundary value problems. Based on the spectral analysis for the Lax pair formulation, we show that the spectral functions can be characterized from the boundary values. We express the solution of the equation in terms of the unique solution of the matrix Riemann–Hilbert problem whose jump matrices are defined by the spectral functions. Moreover, we derive the global algebraic relation that involves the boundary values. In addition, it can be verified that the solution of the elliptic sinh-Gordon equation posed in the semi-strip exists if the spectral functions defined by the boundary values satisfy this global relation.

【 授权许可】

CC BY