Pertubations To Helmholtz Equation

AI Thread Summary
The discussion focuses on finding resources for solving the Helmholtz equations with a perturbation term p(r), specifically in the context of wave equations. Participants express difficulty locating information that addresses p(r) as a non-zero term, as most resources only cover the case where p(r) equals zero. Additionally, there is a request for information on wave equations with perturbations, which are relevant in applications like waveguide optics. A reference to "Kumar's method (perturbation method)" is suggested as a potential resource. The conversation highlights a need for more comprehensive materials on these specific mathematical topics.
gysush
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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
 
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