Spectral and soliton structures of the Sasa–Satsuma higher-order nonlinear Schrödinger equation

In this paper, the Riemann–Hilbert problem of the Sasa–Satsuma higher-order nonlinear Schrödinger equation is investigated, from which spectral and soliton structures are discussed in detail. In addition, an algebra technique is developed to illustrate the soliton structures using Mathematica symbolic computations by choosing suitable parameters, including breather-bell soliton, double-hump soliton, and bell-to-breather soliton interactions. The results show that the spectral and soliton structures of the Sasa–Satsuma higher-order nonlinear Schrödinger equation are more complicated than many other nonlinear Schrödinger type equations.