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.
|Number of pages||11|
|Journal||Theoretical and Mathematical Physics|
|Publication status||Published - Jul 2009|
- elliptic sine-Gordon equation
- nonlinear boundary value problem
- Riemann-Hilbert problem