Inverse scattering for the derivative nonlinear Schrödinger equation with nonzero boundary conditions and triple poles

The inverse scattering transform approach is used to investigate the derivative nonlinear Schrödinger equation (DNLSE) with nonzero boundary conditions (NZBCs) at infinity and triple zeros of analytical scattering coefficients. Based on the analytical, symmetric and asymptotic properties of eigenfunctions, a matrix Riemann–Hilbert problem (RHP) associated with DNLSE with NZBCs is constructed. Then, the reconstruction formula for the potential is found by solving the RHP. In particular, the reflectionless potential with triple poles for the NZBCs is carried out explicitly by means of determinants.