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We continue the study of small amplitude solutions of the damped/driven cubic NLS equation, written as formal series in the amplitude, initiated in our previous work [2]. As in [2], we are interested in behaviour of the formal series under the wave turbulence limit "the amplitude goes to zero, while the space-period goes to infinity".

We consider the damped/driver (modified) cubic NLS equation on a large torus with a properly scaled forcing and dissipation, and decompose its solutions to formal series in the amplitude. We study the second order truncation of this series and prove that when the amplitude goes to zero and the torus' size goes to infinity the energy spectrum of the truncated solutions becomes close to a solution of the damped/driven wave kinetic equation. Next we discuss higher order truncations of the series.

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