ZAKHAROV-SHABAT EQUATIONS FOR DARK SOLITON-SOLUTIONS TO THE NLS EQUATION

For dark soliton solutions of the NLS equation, an inverse scattering transform is redeveloped. Deductions are essentially simplified in ter ms of an auxiliary spectral parameter from the beginning. Equations of inverse scattering transform in the form of Zakharov-Shabat are found to be simpler than those in the form of Marchenko. An explicate expre ssion for the dark N-soliton solution and its asymptotic behaviors in the limits as t --> +/-infinity are simply derived.