The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE

Pelloni, B. (2015) The elliptic sine-Gordon equation: a nonlinear elliptic integrable PDE. In: Fockas, A. S. and Pelloni, B. (eds.) Unified transform: applications and advances. SIAM, pp. 73-90. ISBN 9781611973815

Abstract/Summary

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.