In this paper, we summarise this recent progress to underline the features specific to this nonlinear elliptic case, and we give a new classification of boundary conditions on the semistrip that satisfy a necessary condition for yielding a boundary value problem can be effectively linearised. This classification is based on formulation the equation in terms of an alternative Lax pair.
|Title of host publication||Stock Image Unified Transform for Boundary Value Problems|
|Subtitle of host publication||Applications and Advances|
|Editors||A. S. Fockas, B. Pelloni|
|Number of pages||18|
|Publication status||Published - 2014|
Pelloni, B. (2014). The elliptic sine-Gordon equation - a nonlinear elliptic integrable PDE. In A. S. Fockas, & B. Pelloni (Eds.), Stock Image Unified Transform for Boundary Value Problems: Applications and Advances (pp. 73-90). SIAM.