Understanding Regular and Outgoing Functions in Vector Spherical Wave Functions

[OKY]

I am reading reasearch paper about electrodynamic wave.

In the paper, there is a following description
1. regular function
2. outgoing function

They seem to be related to vector spherical wave function.

What is the "regular function" and "outgoing function"?

I would like to know the book in which I can understand about them.


Best regards

 

[Polyrhythmic]

Could you show us the paper? A context would be valuable.

 

[Bill_K]

When you solve the wave equation (any wave equation - scalar, vector, etc) you must set a boundary condition that says whether the wave is incoming or outgoing. The simplest example is the scalar wave equation with spherical symmetry,

1/r ∂²/∂r² (rφ) - 1/c² ∂²φ/∂t² = 0

The solutions are φ(r,t) = A/r exp i(kx + ωt) + B/r exp i(kx - ωt). If you choose the + sign, the solution is incoming. The - sign is an outgoing solution. Both of them are singular at r = 0, but the solution with A = -B is regular there.

 

[OKY]

Could you show us the paper? A context would be valuable.

The paper (manual document) can be obtained from
the link to "manual" in the below web site.
http://eng.auburn.edu/users/dmckwski/scatcodes/

Around page 4 and 5, they use "regular" and "outgoing".


Thank you in advance.

 

[OKY]

When you solve the wave equation (any wave equation - scalar, vector, etc) you must set a boundary condition that says whether the wave is incoming or outgoing. The simplest example is the scalar wave equation with spherical symmetry,

1/r ∂²/∂r² (rφ) - 1/c² ∂²φ/∂t² = 0

The solutions are φ(r,t) = A/r exp i(kx + ωt) + B/r exp i(kx - ωt). If you choose the + sign, the solution is incoming. The - sign is an outgoing solution. Both of them are singular at r = 0, but the solution with A = -B is regular there.

Thank you very much for the detailed reply.

So, is the "regular" same as "incoming" wave? Why they call "regular"?