Hi all, I have a tricky problem in pertubation theory.(adsbygoogle = window.adsbygoogle || []).push({});

I have a function:

[tex]

f(\vec{r}) = P(\vec{r}) + \left( B(\vec{r}) + b(\vec{r}) \right)^2

[/tex]

where [tex] b(\vec{r}) [/tex] is a small perturbation and is equal to 0 when [tex] P(\vec{r}) = 0 [/tex]

Now, to solve the equation

[tex]

\nabla f(\vec{r}) = 0

[/tex]

for b(r) is fairly straightforward by noting that

[tex]

P + (B + b)^2 = C = B^2

[/tex]

using the fact that P = 0 ==> b = 0. And so,

[tex]

b(\vec{r}) = \frac{-P}{2B}

[/tex]

by expanding the above equation and neglecting the [tex]b^2[/tex] term. Now, my question is how do you solve the inhomogeneous equation:

[tex]

\nabla f(\vec{r}) = \vec{A}(\vec{r})

[/tex]

for b(r) where A is a known vector field with 0 curl?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Perturbation theory to solve diff eq?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**