Demonstration of Inverse Scattering Transform for DNLS Equation

Since the Jost solutions of the DNLS equation does not tend to the free Jost solutioins as |λ|→∞,theusual inverse scattering transform（IST）must be revised.Beside the Kaup and Newell’s approach,we propose a simplerevision in constructing the equations of IST,where the usual Zakharov-Shabat kern is revised by multiplying λ;orλ;.To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations.