Application of the Riemann–Hilbert approach to the derivative nonlinear Schrödinger hierarchy

Abstract

In our paper, we mainly study the [Formula: see text]-soliton solutions for the derivative nonlinear Schrödinger (DNLS) hierarchy. From the spectral problem of the DNLS hierarchy, the associated Riemann–Hilbert problem is constructed. Based on the scattering relationship and solving the Riemann–Hilbert problem, the [Formula: see text]-soliton solutions for the DNLS are given explicitly.