  We present an integrable Hamiltonian which describes the sinh-Gordon model on
the half line coupled to a non-linear oscillator at the boundary. We explain
how we apply Sklyanin's formalism to a dynamical reflection matrix to obtain
this model. This method can be applied to couple other integrable field
theories to dynamical systems at the boundary. We also show how to find the
dynamical solution of the quantum reflection equation corresponding to our
particular example.
