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| →∞, the usual inverse scattering transform (IST) must be revised. Beside the Kaup and Newell's approach, we propose a simple revision in constructing the equations of IST, where the usual Zakharov-Shabat kern is revised by multiplying λ-2 or λ-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations.