Wave turbulence in one-dimensional models

A two-parameter nonlinear dispersive wave equation proposed by Majda, McLau ghlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is t o test the validity of weak turbulence theory. Although weak turbulence the ory is independent on the sign of the nonlinearity of the model, the numeri cal results show a strong dependence on the sign of the nonlinearity, A pos sible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence. (C) 200 1 Published by Elsevier Science B.V.