The Cauchy–Poisson Problem: Application to Tsunami Generation and Propagation

The classical Cauchy-Poisson (C-P) problem is the initial value problem for surface waves. The classical C-P problem as described by Lamb (1945) deals with one-dimensional standing waves in an ocean of infinite depth. Although the classical problem is hardly suitable for tsunami studies, it is simple and can be used to introduce certain concepts. Two different initial states are considered: initial elevation of the free surface with no motion, and a horizontal surface with an initial distribution of surface impulse.