On the basis of the integrable Kaup-Boussinesq version of the shallow
water equations, an analytical theory of undular bores is constructed.
The problem of the decay of an initial discontinuity is considered.
This is a pre-print. The definitive version: EL, G.A. and GRIMSHAW, R.H.J., 2001. Integrable shallow-water equations and undular bores. Studies in Applied Mathematics, 106(2), pp. 157-186