Tao Sixing
School of Mathematics and Statistics, Shangqiu Normal University, Shangqiu 476000, China.
Math Biosci Eng. 2023 May 12;20(7):11978-11997. doi: 10.3934/mbe.2023532.
In this paper, a (2+1)-dimensional KdV4 equation is considered. We obtain Lie symmetries of this equation by utilizing Lie point symmetry analysis method, then use them to perform symmetry reductions. By using translation symmetries, two fourth-order ordinary differential equations are obtained. Solutions of one fourth order ordinary differential equation are presented by using direct integration method and $ (G'/G) $-expansion method respectively. Furthermore, the corresponding solutions are depicted with appropriate graphical representations. The other fourth-order ordinary differential equation is solved by using power series technique. Finally, two kinds of conserved vectors of this equation are presented by invoking the multiplier method and Noether's theorem respectively.
本文考虑了一个(2 + 1)维KdV4方程。我们利用李点对称分析方法获得该方程的李对称性，然后用它们进行对称约化。通过平移对称性，得到了两个四阶常微分方程。分别用直接积分法和(G'/G)展开法给出了一个四阶常微分方程的解。此外，用适当的图形表示法描绘了相应的解。另一个四阶常微分方程用幂级数技术求解。最后，分别通过乘子法和诺特定理给出了该方程的两类守恒向量。
