The multi-soliton and multiple-poles soliton solutions for the six-order nonlinear Schrödinger equation

We present the inverse scattering transform method to the six-order nonlinear Schrödinger equation on the line with zero boundary condition in the form of an appropriate Riemann–Hilbert problem. We solve the associated Riemann–Hilbert problem involving two cases of N simple poles and N multiple higher-order poles, which enables us to obtain the exact formulae of N -soliton and multiple-poles soliton solutions. Furthermore, the dynamic behaviors of various solitons are displayed.