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

Access to Document

10.1007/s11232-009-0094-3

Cite this

@article{5e9e2d3bda7b4e98a7dd31eb8c6e389f,

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.",

keywords = "elliptic sine-Gordon equation, nonlinear boundary value problem, Riemann-Hilbert problem",

author = "Beatrice Pelloni",

year = "2009",

month = jul,

doi = "10.1007/s11232-009-0094-3",

language = "English",

volume = "160",

pages = "1031--1041",

journal = "Theoretical and Mathematical Physics",

issn = "0040-5779",

publisher = "Pleiades Publishing",

number = "1",

}

TY - JOUR

T1 - Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

AU - Pelloni, Beatrice

PY - 2009/7

Y1 - 2009/7

N2 - 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.

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.

KW - elliptic sine-Gordon equation

KW - nonlinear boundary value problem

KW - Riemann-Hilbert problem

U2 - 10.1007/s11232-009-0094-3

DO - 10.1007/s11232-009-0094-3

M3 - Article

SN - 0040-5779

VL - 160

SP - 1031

EP - 1041

JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

IS - 1

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this