In this paper, based on the dynamical system method, we obtain the exact parametric expressions of the travelling wave solutions of the Wu–Zhang system. Our approach is much different from the existing literature studies on the Wu–Zhang system. Moreover, we also study the fractional derivative of the Wu–Zhang system. Finally, by comparison between the integer-order Wu–Zhang system and the fractional-order Wu–Zhang system, we see that the phase portrait, nonzero equilibrium points, and the corresponding exact travelling wave solutions all depend on the derivative order . Phase portraits and simulations are given to show the validity of the obtained solutions.

中文翻译：

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吴张系统行波解的动力学分析

在本文中，基于动力学系统方法，我们获得了Wu-Zhang系统行波解的精确参数表达式。我们的方法与有关Wu-Zhang系统的现有文献研究有很大不同。此外，我们还研究了Wu-Zhang系统的分数导数。最后，通过比较整数阶Wu-Zhang系统和分数阶Wu-Zhang系统，我们发现相像，非零平衡点以及相应的精确行波解均取决于导数阶。给出了相图和仿真，以显示所获得解决方案的有效性。