INTEGRABILITY OF LINEAR AND NONLINEAR EVOLUTION-EQUATIONS AND THE ASSOCIATED NONLINEAR FOURIER-TRANSFORMS

The inverse spectral method is a nonlinear Fourier transform method fo r solving certain equations. Here, we emphasize that such transforms s hould be considered in their own right. We also elucidate further the connection between the Fourier transform and inverse spectral methods by establishing that linear equations can also be solved through the i nverse spectral method.