Integrable boundary interaction in 3D target space: the "pillow-brane"   model
  We propose a model of boundary interaction, with three-dimensional target space, and the boundary values of the field {\vec X}\in R^3 constrained to lay on a two-dimensional surface of the "pillow" shape. We argue that the model is integrable, and suggest that its exact solution is described in terms of certain linear ordinary differential equation. 
Sergei L. Lukyanov and Alexander B. Zamolodchikov
hep-th cond-mat.stat-mech math-ph math.MP