In this paper, the Riemann–Hilbert problem of the modified Korteweg–de Vries (mKdV) equation is studied, from which a new combined soliton solution is obtained. In addition, to illustrate the dynamics of the new combined soliton solution, an algebra technique is developed to demonstrate the soliton interactions using Mathematica symbolic computations. The proposed method is effective in deriving and investigating new soliton solutions of the mKdV equation. The results also expand the understanding of the soliton structure of the mKdV equation.

中文翻译：

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修正 Korteweg-de Vries 方程的新组合孤子解

本文研究了修正的 Korteweg-de Vries (mKdV) 方程的 Riemann-Hilbert 问题，从中得到了一个新的组合孤子解。此外，为了说明新的组合孤子解决方案的动力学，开发了一种代数技术来演示使用 Mathematica 符号计算的孤子相互作用。所提出的方法在推导和研究 mKdV 方程的新孤子解方面是有效的。结果还扩展了对 mKdV 方程孤子结构的理解。