Wave turbulence in one-dimensional models

In this note, we assess the validity of weak turbulence theory by numerical ly investigating a three-parameter nonlinear dispersive wave equation. The predicted power-law solutions are explicitly determined and then compared w ith the numerical results. For both signs of nonlinearity, we show that the weakly turbulent regime is strongly influenced by the presence of coherent structures. These are wave collapses and quasisolitons. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.