This article is cited in 12 papers

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

B. Pelloni

University of Reading

Abstract: We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann–Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Keywords: elliptic sine-Gordon equation, nonlinear boundary value problem, Riemann–Hilbert problem.

DOI: 10.4213/tmf6390

 English version: Theoretical and Mathematical Physics, 2009, 160:1, 1031–1041

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