Abstract In this work, the q-homotopy analysis transform method (shortly q-HATM) which is a combined form of q-homotopy analysis method and Laplace transform method is employed to find numerical solution to the new modified coupled Korteweg–de Vries system. This method allows us to fine-tune the convergence region along with rate of convergence of the obtained series solution by allowing the auxiliary parameters n and ħ to vary. The obtained solution by the proposed method is presented in a refined convergent series form. The numerical results show that only few terms are sufficient to obtain an approximate solution which is accurate, efficient, and reliable. Furthermore, the graphical depictions of the obtained approximate solution of the system are presented.

中文翻译：

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一种研究新的修正耦合 Korteweg-de Vries 系统的强大方法

摘要 在这项工作中，q-同伦分析变换方法（简称 q-HATM）是 q-同伦分析方法和拉普拉斯变换方法的组合形式，用于寻找新的修正耦合 Korteweg-de Vries 系统的数值解。这种方法允许我们通过允许辅助参数 n 和 ħ 变化来微调收敛区域以及获得的级数解的收敛速度。通过所提出的方法获得的解以细化的收敛级数形式呈现。数值结果表明，只需要很少的项就足以得到一个准确、有效、可靠的近似解。此外，还给出了所获得的系统近似解的图形描述。