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 X∈R³$\mathbf{X}\in {\mathbb{R}}^3$ 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.