Single soliton solution to the extended KdV equation over uneven depth
George Rowlands, Piotr Rozmej, Eryk Infeld, Anna Karczewska
TL;DR
This paper investigates how uneven riverbeds affect soliton waves by transforming the governing equations to analyze wave behavior over variable depths, providing insights into wave dynamics in natural water bodies.
Contribution
It introduces an approximate method to transform the extended KdV equation over uneven depths into a flat-bottom equation with known solutions.
Findings
The method allows analysis of solitons over uneven beds.
It provides a way to approximate wave behavior in natural settings.
The approach is applicable to long trenches or banks in rivers and oceans.
Abstract
In this note we look at the influence of a shallow, uneven riverbed on a soliton. The idea consists in approximate transformation of the equation governing wave motion over uneven bottom to equation for flat one for which the exact solution exists. The calculation is one space dimensional, and so corresponding to long trenches or banks under wide rivers or else oceans.
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