摘要
In this work,we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger(DNLS)equation.By establishing a matrix Riemann-Hilbert problem and reconstructing potential function q(x,t)from eigenfunctions{Gj(x,t,η)}3/1 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.
基金
This work is supported by the Natural Science Foundation of China(Nos.11601055,11805114 and 11975145)
the Natural Science Research Projects of Anhui Province(No.KJ2019A0637)
University Excellent Talent Fund of Anhui Province(No.gxyq2019096).
