  We give a complete classification of the traveling waves of the following
quadratic Szeg{\"o} equation : $i \partial\_t u = 2J\Pi(|u|^2)+\bar{J}u^2,
\quad u(0, \cdot)=u\_0$, and we show that they are given by two families of
rational functions, one of which is generated by a stable ground state. We
prove that the other branch is orbitally unstable.
