The cubically nonlinear Schro¨dinger equation model of Langmuir turbulence is solved in the weak turbulence limit. Steady‐state power‐law solutions for the energy spectra are found in arbitrary dimensionality. In one spatial dimension, the theory incorrectly predicts that no spectrum evolves in time. In three spatial dimensions, numerical solutions are obtained for the undriven, undamped, initial value problem and for the driven, damped, initial value problem.