The bound-state soliton solutions of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system

The inverse scattering of a higher-order nonlinear Schrödinger equation for inhomogeneous Heisenberg ferromagnetic system with zero boundary condition is calculated by an appropriate Riemann–Hilbert (RH) problem. The RH problem of reflection coefficient with multiple high-order poles is obtained. Meanwhile, the calculation formulas of bound-state (BS) solitons and multiple BS solitons corresponding to one high-order pole and multiple high-order poles are also calculated, respectively. Finally, the corresponding soliton solution model is calculated according to the corresponding formula. Simultaneously, we also obtain the BS soliton, the multiple BS soliton and the interaction between multiple BS solitons and multiple BS solitons.