Today, most of the real physical world problems can be modeled with variable-coefficient KdV–modified KdV (vcKdV–mKdV) equation. Besides, the solution methods and their reliabilities are the most important. Therefore, a high precision numerical method is always needed. In this paper, Fourier spectral method is applied to solve the space fractional generalized vcKdV–mKdV equation and the influence of fractional orders on numerical solution of the space fractional generalized vcKdV–mKdV equation is investigated. Numerical simulations in different situations of equation are conducted, including the propagation and interaction of the generalized ball-type, kink-type and periodic-depression solitons. From the numerical experiments pondered here and compared with the other methods, it is found that the numerical solutions match well with the exact solutions, which demonstrate that the Fourier spectral method is a satisfactory and efficient algorithm.

中文翻译：

---

用傅里叶光谱法求解空间分数变系数 KdV 修正的 KdV 方程的数值解

今天，大多数现实物理世界的问题都可以用可变系数 KdV 修正的 KdV (vcKdV-mKdV) 方程来建模。此外，解决方法及其可靠性是最重要的。因此，始终需要一种高精度的数值方法。本文采用傅里叶谱法求解空间分数广义vcKdV-mKdV方程，研究分数阶对空间分数广义vcKdV-mKdV方程数值解的影响。进行了不同方程情况下的数值模拟，包括广义球型、扭结型和周期凹陷孤子的传播和相互作用。从这里思考的数值实验和与其他方法的比较，