Simultaneous spacetime scaling symmetry of the wave equation
= Simultaneous spacetime scaling symmetry of the wave equation
The flow of $V=t\partial_t+x\partial_x$ is $(t,x,u)\mapsto(e^\epsilon t,e^\epsilon x,u)$. Its second prolongation scales both $u_{tt}$ and $u_{xx}$ with weight minus two, so it preserves $u_{tt}-u_{xx}=0$.