The fundamental problem of inverse scattering method in solving the DNLS equation
求解DNLS方程的反散射法的基本问题

This is a basic work on the inverse scattering transform that constructs the complete orthonormal system of the free Jost solution. In order to establish the system for the DNLS equation, we introduce a new transform for the spectral parameter and a gauge transform. The Marchenko's equation and the Zakharov-Shabat's equation of inverse scattering are derived based on the new spectral parameter.