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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Reading, Reading, UK

    B. Pelloni

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  1. B. Pelloni
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Correspondence to B. Pelloni.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 189–201, July, 2009.

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Pelloni, B. Spectral analysis of the elliptic sine-Gordon equation in the quarter plane. Theor Math Phys 160, 1031–1041 (2009). https://doi.org/10.1007/s11232-009-0094-3

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  • DOI: https://doi.org/10.1007/s11232-009-0094-3

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