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We investigate the stationary state of a model system evolving according to amodified focusing truncated nonlinear Schr\"odinger equation (NLSE) used todescribe the envelope of Langmuir waves in a plasma. We restrict the system tohave a finite number of normal modes each of which is in contact with aLangevin heat bath at temperature $T$. Arbitrarily large realizations of thefield are prevented by restricting each mode to a maximum amplitude. Weconsider a simple modeling of wave-breaking in which each mode is set equal tozero when it reaches its maximum amplitude. Without wave-breaking thestationary state is given by a Gibbs measure. With wave-breaking the systemattains a nonequilibrium stationary state which is the unique invariant measureof the time evolution. A mean field analysis shows that the system exhibits atransition from a regime of low field values at small $|\lambda|$, to a regimeof higher field values at large $|\lambda|$, where $\lambda<0$ specifies thestrength of the nonlinearity in the focusing case. Field values at large$|\lambda|$ are significantly smaller with wave-breaking than withoutwave-breaking.

Nonequilibrium stationary state of a truncated stochastic NLSE: I. Formulation and mean field approximation