Pertubations To Helmholtz Equation

[gysush]

Consider the Helmholtz Equations with a perturbation p(r)

[gradient^2 + p(r) + omega^2/c(r)^2 ]u(r,w) = 0

Does anyone know where I can find resources to the solutions/discussion of this equation? I can find many things such that p(r) = 0 , but the RHS = forcing function, but that is not what I want.

Likewise, any resources pertaining to the wave equation with a perturbation would also be nice

[gradient^2 + p(r) - 1/c(r)^2 * del^2/delT^2]u(r,t) = 0

 

[sugeet]

it is used in many places, for example in waveguide optics, we do the same, you could look up at "Kumar`s method (perturbation method)", this link might be useful! http://www.opticsinfobase.org/ol/fulltext.cfm?uri=ol-8-1-63&id=7914