In your point of view, is it possible to include the terms of variation of the geometry of a channel in the analytical expression of the Serre-Green-Naghdi soliton?
The geomorphic relationships known as hydraulic geometry In general Hydraulic geometry deals with variation in channel characteristics in relation to variations in discharge. Two sets of variations take place: variations at a particular cross section (at-a-station) and variations along the length of the stream (downstream variations). Characteristics responsive to analysis by hydraulic geometry include width (water-surface width), depth (mean water depth), velocity (mean velocity through the cross section), sediment (usually concentration or transport, or both, of suspended sediment), downstream slope, and channel friction.
This paper can help you Article Generalised Serre-Green-Naghdi equations for open channel an...