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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)1031-1041
Number of pages11
JournalTheoretical and Mathematical Physics
Volume160
Issue number1
DOIs
Publication statusPublished - Jul 2009

Keywords

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

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