Which equation describes surface waves in a fluid on the same scale?

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TL;DR
Trying to get the name of an equation for free surface flow.
When considering surface waves in a fluid in 3D, there are a number of assumptions the easiest one is to take the "thin wave" approximation which yields a Kadomtsev-Petviashvilli equation. I'm looking for the name of the equation(or set of equations) for when the x and y are of the same scale. Does anyone know what it's called?
 
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