While the classical inverse scattering method is used to solve integrable partial differential equations which model continuous media (for example, the KdV equation models shallow water waves), the QISM is used to solve many-body quantum systems, sometimes known as spin chains, of which the Heisenberg spin chain is the best-studied and most famous example. These are typically discrete systems, with particles fixed at different points of a lattice, but limits of results obtained by the QISM can give predictions even for field theories defined on a continuum, such as the quantum sine-Gordon model.