1
$\begingroup$

I am having a lot of trouble understanding the method of characteristics to solve the wave equation.

In fact, I have a final exam tomorrow and I can't seem to get a question from a previous assignment. I know Math.SE isn't really meant for this kind of stuff but I am hoping someone would just briefly explain how my professor is getting the solution. I appreciate it.

Here is the problem: $\frac{\partial^2 u}{\partial t^2} - 9 \frac{\partial^2 u}{\partial x^2} = 0$ on the real axis (i.e., $-\infty < x < \infty$).

Here is the solution. It is a PDF to the professor's solution file.

The solution is on page 3 (question number 3).

I need to know how he's getting his solutions at different times.

  • 1
    The solution your professor gave is via d'Alembert's integral formula. While it *can* be derived via the method of characteristics, one [can also do it via a change of coordinates](http://williewong.wordpress.com/2011/05/12/decay-of-waves-iia-minkowski-background-homogeneous-case/) and many other methods. Is your question that you don't see how he arrived at the d'Alembert formula?2011-12-11

0 Answers 0