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

Yongyi Gu; Najva Aminakbari; Yongyi Gu; Najva Aminakbari

doi:10.3934/math.2020257

AIMS Mathematics

2020, Volume 5, Issue 4: 3990-4010. doi: 10.3934/math.2020257

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Research article

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

Yongyi Gu ^{1,2
,
,},
Najva Aminakbari ³

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

Received: 28 December 2019 Accepted: 17 April 2020 Published: 26 April 2020
MSC : 30D35, 34A05, 35C07

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.
- differential equation,
- KdV-Sawada-Kotera equation,
- symbolic computation,
- extended complex method,
- exp(-ψ(z))-expansion method
Citation: Yongyi Gu, Najva Aminakbari. Two different systematic methods for constructing meromorphic exact solutions to the KdV-Sawada-Kotera equation[J]. AIMS Mathematics, 2020, 5(4): 3990-4010. doi: 10.3934/math.2020257

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Abstract

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.

References

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