What does scattering to infinity mean for wave equation solutions?

[dcs23]

What does this term mean? In particular a solution of the wave equation scattering to infinity?

 

[jtbell]

I have no idea. I've never seen the phrase "energy scattering." Can you give an exact quotation from where you saw it?

Are you perhaps trying to translate something into English from another language?

 

[dcs23]

http://www.springerlink.com/content/6416t44172742218/

This is the paper that I was reading. All in English.

Thanks

 

[Andy Resnick]

It looks like the author is starting with the Laplace equation, which usually indicates wave processes, such as electromagnetic waves. The paper could be discussing one of a few things.

1) It could be simply determining existence conditions for stable scattering solutions.

2) AFAIK, the radiometric model of coherence is an underdetermined problem; this paper could represent work trying to better model how coherent light propogates.

My guess is that it's #1.

 

[dcs23]

Ah ok, well I was trying to determine whether or not the wave equations always produces solutions without singularities, if not then when? Working in 1D.

I would be very grateful for any help!

 

[Andy Resnick]

Actually, light scattering often produces singularities. These can be caustics, morphology-dependent resonances, and other phenomena.

Edit: I should clarify- those singularities occur in 2 or 3 dimensions (maybe more than 3, but I'm not concerned with those). Don't know if they can occur in 1 dimension. For a while I was reading about catastrophe theory, and I think you need at least 2 dimensions for a caustic.