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

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The discussion focuses on surface waves in a fluid in three dimensions, specifically under the "thin wave" approximation that leads to the Kadomtsev-Petviashvilli equation. The user seeks information about the equations applicable when the x and y dimensions are of the same scale. There is a request for the specific name of these equations. Participants are encouraged to share insights or references related to this topic. The conversation emphasizes the need for clarity on equations governing surface waves in equal dimensional scales.
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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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