A note on late-time tails of spherical nonlinear waves
  We consider the long-time behavior of small amplitude solutions of the semilinear wave equation $\Box \phi =\phi^p$ in odd $d\geq 5$ spatial dimensions. We show that for the quadratic nonlinearity ($p=2$) the tail has an anomalously small amplitude and fast decay. The extension of the results to more general nonlinearities involving first derivatives is also discussed. 
Piotr Bizo\'n, Tadeusz Chmaj, Andrzej Rostworowski