# Variable change in this partial differential equation

I'm supposed to solve this: $$u_{tt}-a\left(u_{rr}+\frac{u_r}{r}\right)=0$$ Doing some variable change to leave it as the simplest wave equation: $$v_{tt}-av_{rr}=0$$. $a$ is a positive parameter. I've been trying lots of changes and I can't get the right one.

The thing is to study the evolution of a wave with cylindrical symmetry, $$u_{tt}-v^2\nabla^2u=0$$ Developing the laplacian in cylindrical coordinates gets you my first equation.

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You can't. Solution of wave equation in cylindrical coordinates are superposition of Bessel functions. –  Kaster Feb 27 '13 at 19:19
@Kaster Ok thanks. –  MyUserIsThis Feb 27 '13 at 19:23