Eikonal equation (method of characteristics)

Question

U_x²+U_y²=[n(y)]²  , where n(y)=n₀(1+ky). How do I proceed use method of characteristics to solve Eikonal equation when                                                                 it is not = to 1?

 

 

Answer 1

Hi Ben!

 

It may be better to ask this as a math question, since you are looking to convert your PDE into an ODE along some characteristic curve that you have to discover.  This is, admittedly, not my area of expertise, but I can see what I can find out with a little research.