Geodesic
Spectral analysis of the~elliptic sine-Gordon equation in the~quarter plane
Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 189-201

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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.
Mots-clés : elliptic sine-Gordon equation
Keywords: nonlinear boundary value problem, Riemann–Hilbert problem. 
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     author = {B. Pelloni},
     title = {Spectral analysis of the~elliptic {sine-Gordon} equation in the~quarter plane},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {189--201},
     publisher = {mathdoc},
     volume = {160},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a17/}
}
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B. Pelloni. Spectral analysis of the~elliptic sine-Gordon equation in the~quarter plane. Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 1, pp. 189-201. http://geodesic.mathdoc.fr/item/TMF_2009_160_1_a17/