Shock waves dominate in a wide variety of fields in physics dealing
with nonlinear phenomena, nevertheless the description of their evolution is not
resolved for the entire dynamics. Here we propose an analytical method based on
Gamow vectors, which belong to irreversible quantum mechanics. We theoretically
and experimentally show the appearance of these decaying states during shock evolution
allowing to describe the whole wave propagation. These results open new ways
to the control of extreme nonlinear regimes such as supercontinuum generation or
in the analogies of fundamental physical theories.