Models for small amplitude, long wavelength, long crested water waves (waves that propagate primarily in one direction) have been studied extensively after the introduction of the Boussinesq equations in the 1870s, which are partial differential equations (PDEs) derived as approximations of the Euler equations that generally describe adiabatic, inviscid fluid flow. A plethora of Boussinesq-type models for uni- and bi-directional waves have since been proposed, the most famous being the Korteweg-de Vries (KdV) equation, as well as the more recently discovered class of abcd-systems of PDEs, of which a notable example is the Kaup-Broer system. A common method for solving such problems is the Inverse Scattering Transform (IST), which will be discussed in detail along with a novel algorithm for computing the spectra of an N-soliton solution of the KB-system.

This is joint work with Patrik Nabelek, Solomon Yim, Peter Prins (TU Delft), and Sander Wahls (KIT).