Implementing circular wave with Gerstner equations.


I am implementing circular waves based on Gerstner equations.
I used the equations and everything works fine. The issue is that I want a single wave propagating from the center to the edges of the surface and using the equations I get all my surface deformed. I tried to modify only the z position of vertices which have the (x, y) between two concentric circles which both expand with the speed of the wave and the distance between them is the wavelength. It seems to work well but when I zoom in, the edges of the wave (which are the edges of the circles) appear pixelated.
Is there another way to render just one wave without getting all my surface deformed?

P.S.: This is my firs post here. Sorry if I post in the wrong section.