AIMS Mathematics, 2020, 5(4): 3990-4010. doi: 10.3934/math.2020257

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Two different systematic methods for constructing meromorphic exact solutions to the KdV-Sawada-Kotera equation

1 Big data and Educational Statistics Application Laboratory, Guangdong University of Finance and Economics, Guangzhou 510320, China
2 School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China
3 School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

In this paper, we obtain meromorphic exact solutions of the KdV-Sawada-Kotera equation via two different systematic methods. Applying the exp(-ψ(z))-expansion method, we achieve the trigonometric, exponential, hyperbolic and rational function solutions for the mentioned equation. It is more interesting that we firstly proposed the extended complex method based on the previous work of Yuan et al., and as an example we use it to search exact solutions to the KdV-Sawada-Kotera equation. Dynamic behaviors of solutions obtained by these two different systematic techniques are also shown by some graphs. The results show that these two methods are direct and efficient methods to deal with various differential equations in the applied sciences.
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