We investigate the stationary state of a model system evolving according to a modified focusing truncated nonlinear Schrodinger equation (NLSE) used to describe the envelope of Langmuir waves in a plasma. We restrict the system to have a finite numbe
r of normal modes each of which is in contact with a Langevin heat bath at temperature $T$. Arbitrarily large realizations of the field are prevented by restricting each mode to a maximum amplitude. We consider a simple modeling of wave-breaking in which each mode is set equal to zero when it reaches its maximum amplitude. Without wave-breaking the stationary state is given by a Gibbs measure. With wave-breaking the system attains a nonequilibrium stationary state which is the unique invariant measure of the time evolution. A mean field analysis shows that the system exhibits a transition from a regime of low field values at small $|lambda|$, to a regime of higher field values at large $|lambda|$, where $lambda<0$ specifies the strength of the nonlinearity in the focusing case. Field values at large $|lambda|$ are significantly smaller with wave-breaking than without wave-breaking.
