Inverse Scattering Transform in Squared Spectral Parameter for DNLS Equation under Vanishing Boundary Conditions

After a transformation, the inverse scattering transform for the derivative nonlinear Schrödinger (DNLS) equation is developed in terms of squared spectral parameter. Following this approach, we obtain the orthogonality and completeness relations of free Jost solutions, which is impossibly constructed with usual spectral parameter in the previous works. With the help these relations, the Zakharov--Shabat equations as well as Marchenko equations of IST are derived in the standard way.