The traveling wave solutions of the combined Korteweg de Vries-modified Korteweg de Vries (cKdV-mKdV) equation and a complexly coupled KdV (CcKdV) equation are obtained by using the auto-Bäcklund Transformation Method (aBTM). To numerically approximate the exact solutions, the Finite Difference Method (FDM) is used. In addition, these exact traveling wave solutions and numerical solutions are compared by illustrating the tables and figures. Via the Fourier–von Neumann stability analysis, the stability of the FDM with the cKdV–mKdV equation is analyzed. The [Formula: see text] and [Formula: see text] norm errors are given for the numerical solutions. The 2D and 3D figures of the obtained solutions to these equations are plotted.

中文翻译：

---

非线性动力学中行波解的比较精确和数值模拟

组合的 Korteweg de Vries 修正 Korteweg de Vries (cKdV-mKdV) 方程和复耦合 KdV (CcKdV) 方程的行波解是通过使用自动 Bäcklund 变换方法 (aBTM) 获得的。为了在数值上逼近精确解，使用了有限差分法 (FDM)。此外，这些精确的行波解和数值解通过表格和图形进行了比较。通过傅里叶-冯诺依曼稳定性分析，分析了具有 cKdV-mKdV 方程的 FDM 的稳定性。给出了数值解的 [公式：见正文] 和 [公式：见正文] 范数误差。绘制了这些方程获得的解的 2D 和 3D 图。