- #1
ozone
- 122
- 0
Hello all,
I have boiled a very long physics problem down to the point that I need to solve the coupled equations
[tex] \frac{\partial^2 x}{\partial u^2} + xf(u) + yg(u) = 0 [/tex]
[tex] \frac{\partial^2 y}{\partial u^2} + yf(u) - xg(u) = 0 [/tex]
We may assume that[tex] |f| ,|g| << 1.[/tex] and that both f and g are periodic on the same interval T, i.e. [tex]f(u) = f(u+T),g(u) = g(u+T)[/tex]
I was wondering if this is something that could be solved with little knowledge of perturbation theory or if this was a very advanced problem, and I was wondering if anyone had any useful resources. So far I have found that this would be relatively easy to solve if they weren't coupled, but this is a level of complexity which is beyond me
Thank you.
I have boiled a very long physics problem down to the point that I need to solve the coupled equations
[tex] \frac{\partial^2 x}{\partial u^2} + xf(u) + yg(u) = 0 [/tex]
[tex] \frac{\partial^2 y}{\partial u^2} + yf(u) - xg(u) = 0 [/tex]
We may assume that[tex] |f| ,|g| << 1.[/tex] and that both f and g are periodic on the same interval T, i.e. [tex]f(u) = f(u+T),g(u) = g(u+T)[/tex]
I was wondering if this is something that could be solved with little knowledge of perturbation theory or if this was a very advanced problem, and I was wondering if anyone had any useful resources. So far I have found that this would be relatively easy to solve if they weren't coupled, but this is a level of complexity which is beyond me
Thank you.
Last edited: