The bound-state soliton solutions of the complex modified KdV equation

The inverse scattering method is performed to the complex modified Korteweg–de Vries equation with zero boundary condition by developing an appropriate Riemann–Hilbert problem (RHP). We solve the RHP when reflection coefficient has multiple higher-order poles, and display the formulae of bound-state (BS) solitons and multiple BS solitons which correspond to one higher-order pole and multiple higher-order poles, respectively. The patterns of the BS solitons are shown and the interactions between solitons and BS solitons are considered.