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.

中文翻译：

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复修正 KdV 方程的束缚态孤子解

通过开发适当的 Riemann-Hilbert 问题 (RHP)，对具有零边界条件的复杂修正 Korteweg-de Vries 方程执行逆散射方法。我们求解反射系数有多个高阶极点时的 RHP，并给出了分别对应一个高阶极点和多个高阶极点的束缚态 (BS) 孤子和多个 BS 孤子​​的公式。显示了 BS 孤子​​的模式，并考虑了孤子和 BS 孤子​​之间的相互作用。