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Laplacian acts like Divergence but not completely. If you take a function (called $\vec{A}$) and write that laplacian of that function is $0$ than it will be flat space. $$\nabla^2\vec{A}=0$$ But...
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#1: Initial revision
Laplacian acts like Divergence but not completely. If you take a function (called $\vec{A}$) and write that laplacian of that function is $0$ than it will be flat space.
$$\nabla^2\vec{A}=0$$
But if you write Laplacian like this :
$$\Delta \vec{A}=\text{c}\frac{\partial^2 \vec A}{\partial t^2}$$
than it will represent a wave.
Divergence of gradient actually means "changes in field with respect to that field".
In short we can say that Laplacian represent curvature or stress of the field.