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 usualinverse scattering transform (IST) must be revised. Beside the Kaupand Newell's approach, we propose a simple revision in constructingthe equations of IST, where the usual Zakharov-Shabat kern is revisedby multiplying λ^-2 or λ^-1. To justify the revision we show that the Jost solutions obtained do satisfy the pair of compatibility equations.