Traveling Wave on Circular Membrane

[sharklasers45]

Homework Statement

Is it possible to find a solution to the wave equation on a circular membrane such that the shape remains constant, but rotates at a fixed rate in the angular direction?

Homework Equations

The Attempt at a Solution

I've tried separating variables, and assuming the solution only depends on theta, but the time dependence is oscillatory (which comes out of the normal separation of variables process), so this doesn't represent rotation in time.

And by writing the wave equation in polar coordinates, I can't get rid of the r dependence even if I assume the d/dr derivatives are 0 because of the 1/r^2 multiplying the theta derivative...

 

[christoff]

I took a course in bifurcation theory from a guy who does research into spiral waves and symmetry breaking, and he talked about this a little bit at the end. I don't know exactly what your PDE looks like, but I seem to remember that explicitly solving this kind of equation doesn't work out very well.

You might consider writing down some equations if you really want our help. What exactly are you starting with, what did you do, where are you stuck? Use LaTeX.