  We have very little experience of the quantum dynamics of the ubiquitous
nonlinear waves. Observed phenomena in high energy physics are perturbations to
linear waves, and classical nonlinear waves, like solitons, are barely affected
by quantum effects. We know that solitons, immutable in classical physics,
exhibit collapse and revivals according to quantum mechanics. However this
effect is very weak and has never been observed experimentally. By predicting
black hole evaporation Hawking first introduced a distinctly quantum effect in
nonlinear gravitational physics.Here we show the existence of a general and
universal quantum process whereby a soliton emits quantum radiation with a
specific frequency content, and a temperature given by the number of quanta,
the soliton Schwarzschild radius, and the amount of nonlinearity, in a precise
and surprisingly simple way. This result may ultimately lead to the first
experimental evidence of genuine quantum black hole evaporation. In addition,
our results show that black hole radiation occurs in a fully quantised theory,
at variance with the common approach based on quantum field theory in a curved
background; this may provide insights into quantum gravity theories. Our
findings also have relevance to the entire field of nonlinear waves, including
cold atomic gases and extreme phenomena such as shocks and rogue-waves.
Finally, the predicted effect may potentially be exploited for novel tunable
quantum light sources.
