Abstract The KdV equation is one of the most famous PDE which has a vast field of applications in fluid dynamics. The scope of our research is the Lie group analysis of time-fractional KdV-type equation including a perturbation term. Thus, the Lie group theory is extended to both cases simultaneously. Geometric vector fields of symmetries and one-dimensional optimal system are found in order to reduce the equation. Finally, approximated conservation laws are given via modified Ibragimov’s theorem.

中文翻译：

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小摄动参数时分三阶KdV型方程的李群分析及守恒定律

摘要 KdV 方程是最著名的偏微分方程之一，在流体动力学中有广泛的应用。我们的研究范围是包括微扰项的时间分数阶 KdV 型方程的李群分析。因此，李群理论同时扩展到这两种情况。找到了对称的几何向量场和一维最优系统，以减少方程。最后，通过修正的 Ibragimov 定理给出近似守恒定律。