Convergence of the pseudospectral method for the Ginzburg-Landau equation (Q915008)

The convergence of the pseudospectral (Fourier) method for the one- dimensional Ginzburg-Landau wave equations \[ iA_ t+(1-ic_ 0)A_{xx}=i\frac{c_ 0}{c_ 1}A-(1+i\frac{c_ 0}{c_ 1})| A|^ 2A \] is established for the parameter regimes \(c_ 0,c_ 1>0\) and \(c_ 0>0\), \(c_ 1<0\). The rate of convergence depends on the smoothness of the initial data.