On the Riemann-Hilbert problem of a generalized derivative nonlinear Schrodinger equation

In this work, we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrodinger (DNLS) equation. By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x, t) from eigenfunctions {G(j) (x, t, h)}(1)(3) 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 (eta), s(eta), F(eta), S(eta) 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.