Shallow Water Equations and Initial Conditions

[TheFerruccio]

I have seen lots of simulations using the shallow water equations, and every one I've seen involves having some sort of initial displacement in the water, resulting in a propagation of waves through a medium of either constant or variable depth, as a function of position.

However, can you reverse this? As in, can you just have the initial conditions for the surface of the water be completely flat, then have a perturbation in the depth of the water, showing how the waves propagate in that manner?

 

[Studiot]

What you are seeking is Russell's experiment (1834).

You need to look up solitons and the Kortweg-de Vries equation

Solitons an Introduction

Drazin and Johnson

Cambridge University Press