In this work, we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrdinger (DNLS) equation. By establishing a matrix Riemann–Hilbert problem and reconstructing potential function q(x, t) from eigenfunctions in the inverse problem, the initial-boundary value problems for the generalized DNLS equation on the half-line are discussed. Moreover, we also obtain that the spectral functions f(η), s(η), F(η), S(η) are not independent of each other, but meet an important global relation. As applications, the generalized DNLS equation can be reduced to the Kaup–Newell equation and Chen–Lee–Liu equation on the half-line.

在这项工作中，我们直接针对广义导数非线性Schrdinger（DNLS）方程使用逆散射方法提出了一种统一的变换方法。通过建立矩阵黎曼-希尔伯特问题并从反问题中的本征函数重建势函数q（x，t），讨论了半线上广义DNLS方程的初边值问题。此外，我们还获得了光谱函数f（η），s（η），F（η），S（η）不是彼此独立的，而是满足重要的全球关系。作为应用，可以将广义DNLS方程简化为半线上的Kaup-Newell方程和Chen-Lee-Liu方程。