In this article, analytical and numerical solutions to the simplified modified Camassa–Holm (MCH) equation by using the Riccati–Bernoulli (RB) sub-ODE method and moving mesh method are obtained. Some new solutions are given. The discrtisation of the presented model is introduced in the form of finite difference operators. Some 3D graphs for the presented solution are plotted with the aid of the Matlab software for suitable values of parameters. We introduce the comparison between numerical and exact solutions.

中文翻译：

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修正的 Camassa-Holm 方程的解析和数值研究

在本文中，使用 Riccati-Bernoulli (RB) sub-ODE 方法和移动网格方法获得了简化的修正 Camassa-Holm (MCH) 方程的解析解和数值解。给出了一些新的解决方案。所提出模型的离散化以有限差分算子的形式引入。所提出的解决方案的一些 3D 图形是在 Matlab 软件的帮助下绘制的，以获得合适的参数值。我们介绍了数值解和精确解之间的比较。