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

Beatrice Pelloni

doi:10.1007/s11232-009-0094-3

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

Beatrice Pelloni

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1031-1041
Number of pages	11
Journal	Theoretical and Mathematical Physics
Volume	160
Issue number	1
DOIs	https://doi.org/10.1007/s11232-009-0094-3
Publication status	Published - Jul 2009

Keywords

elliptic sine-Gordon equation
nonlinear boundary value problem
Riemann-Hilbert problem

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10.1007/s11232-009-0094-3

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title = "Spectral analysis of the elliptic sine-Gordon equation in the quarter plane",

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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AB - 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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KW - nonlinear boundary value problem

KW - Riemann-Hilbert problem

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DO - 10.1007/s11232-009-0094-3

M3 - Article

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JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

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ER -

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

Abstract

Keywords

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