What is the Meaning of the Eikonal Equation?

[Asuralm]

Dear all:

I have met a equation called Eikonal equation which is a special case of Hamilton-Jacobi equation. It is written as:

||\nablaf(x)|| = P(x)

Could anybody explain what's the meaning of this function please? I have read it from Wiki and mathworld, but it doesn't make too much sense to me.

Thanks in advance.

 

[Dale12]

You can find some details in Godstein's <<Classical Mechanics>> or Landau's <<THe Classical Theory of Fields>>, Good Luck!