Integrable systems as nonlinear realizations of infinite-dimensional symmetries: The Liouville equation example

The Liouville equation is shown to have a natural interpretation in terms of the nonlinear realization of an infinite parameter conformal group in 1+1-dimensions. The relevant zero-curvature representation and Bäcklund transformations get a simple treatment in this approach. The proposed construction can hopefully be generalized to other integrable systems.