- #1

MathematicalPhysicist

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- TL;DR Summary
- On page 211 in equation (9.32) we have a nonlinear equation that ##f## and ##g## should satisfy, which is ##\ddot{f}/f+\ddot{g}/g=0##.

The suggested solution in the book doesn't make sense, can you help me understand it?

Continuing the summary, the author argues that if ##g## is nearly 1, i.e ##g(u)\approx 1+\epsilon(u)##, one obtains the solution:

##f(u)\approx 1-\epsilon(a)##.

The derivative in the summary, i.e the dots represent derivatives with respect to ##u##.

Then how to deduce the solution for ##f##?

If I plug ##g## back to the equation in the summary I get:

$$\ddot{f}+(\ddot{\epsilon}/(1+\epsilon(u)))f=0$$

Don't see how to continue from here, he talks about Fourier representation, but I don't follow his reasoning.

Thanks!

##f(u)\approx 1-\epsilon(a)##.

The derivative in the summary, i.e the dots represent derivatives with respect to ##u##.

Then how to deduce the solution for ##f##?

If I plug ##g## back to the equation in the summary I get:

$$\ddot{f}+(\ddot{\epsilon}/(1+\epsilon(u)))f=0$$

Don't see how to continue from here, he talks about Fourier representation, but I don't follow his reasoning.

Thanks!