Shelf Response KdV

A function to calculate the shelf response at the coast to an incident KdV soliton impulse.

%Calculates the Shelf Response to an incident KdV soliton pulse. Modified version of the analytical model presented in the article: A Model for the Generation of Coastal Seiches
by Deep-Sea Internal Waves. J. Phys. Oceanogr.,20,1459-1467.doi: http://dx.doi.org/10.1175/1520-0485(1990)020<1459:AMFTGO>2.0.CO;2 The authors explain their model using these words:
"The incident internal pulse at the interface generates a surface pulse at the shelf break with amplitude Q0/2 which travels across the shelf toward the coast. It's amplitude doubles
to Q0 at the coast where it reflects from the coastal wall and travels back across the shelf toward the shelf break. Upon reaching the shelf break, part of the pulse is reflected shoreward while part continues into the deep ocean leaking energy to deep-ocean surface and internal waves." The incident pulse is a negative KdV soliton. The soliton amplitude can be set. The shelf depth and length, the deep-ocean upper layer depth, lower layer depth, total depth and respective densities can be changed to typical measured values.
Restriction: the shelf depth is less than the deep-ocean upper layer depth: S < H1. To get the dimensional values of eta_s and zeta_pulse multiply each by eta_i; for u_s multiply by sqrt(g/H)*eta_i.