Coupling the Sine-Gordon Field Theory to a Mechanical System at the   Boundary
  We describe an integrable system consisting of the sine-Gordon field, restricted to the half line, and coupled to a non-linear oscillator at the boundary. By extension of the coupling constant to imaginary values we also outline the equivalent system for the sinh-Gordon field. We show how Sklyanin's formalism can be applied to situations with dynamic boundary conditions, and illustrate the method with the derivation of our example system. 
P. Baseilhac, G. W. Delius and A. George