2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80141We 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.9 pages, Contribution to the proceedings of the NATO Advanced Research Workshop on Statistical Field Theories 2001Exactly Solvable and Integrable Systemstext