The Korteweg-de Vries equation is a partial differential equation that can be used to describe water waves. A few years back, a modified version of this equation was derived, to take Coriolis forces into account. Before that, the Korteweg-de Vries equation had also been found in the realm of Lie theory, as an equation of motion on the Virasoro-Bott group.
This paper aimed to find a relation between the two equation, through studying the equations themselves, as well as through the Lie algebras in which they also appear. This way, two similar transformations from solutions of one equation, to solutions of the other have been found. Both of these come down to a vertical shift, though different ones. Another transformation was also found for the equation, but no similar transformation between the Lie algebras was found.