TRAVELING WAVES OF THE KDV-NKDV EQUATION

Xueqiong Yi; Yuqian Zhou; Qian Liu

doi:10.11948/20230100

2023 Volume 13 Issue 6

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Xueqiong Yi, Yuqian Zhou, Qian Liu. TRAVELING WAVES OF THE KDV-NKDV EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3461-3476. doi: 10.11948/20230100

Citation:

Xueqiong Yi, Yuqian Zhou, Qian Liu. TRAVELING WAVES OF THE KDV-NKDV EQUATION[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3461-3476. doi: 10.11948/20230100

TRAVELING WAVES OF THE KDV-NKDV EQUATION

1.
College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, Sichuan, China
2.
College of Mathematics, Southwest Minzu University, Chengdu, Sichuan 610041, China

Author Bio: Email: xueqiongyi@163.com(X. Yi); Email: cs80liuqian@aliyun.com(Q. Liu)
Corresponding author: Email: cs97zyq@aliyun.com(Y. Zhou)
Fund Project: This research is partially supported by the Sichuan Science and Technology Program (Grant Nos. 23ZYZYTS0425 and 22ZYZYTS0065)

Abstract

Abstract

In this paper, we use the dynamical system method to investigate the wave solutions of the KdV-nKdV equation. We prove Wazwaz’s proposal that the KdV-nKdV equation has continuous periodic wave solutions and give their exact expressions by elliptic integral theory. We confirm that the KdV-nKdV equation has no classical solitary wave solution although it can be regarded as a fusion of the KdV equation with classical solitary wave and the nKdV equation. In addition, we obtain some novel traveling wave solutions of it including trapezoidal wave, inverted ‘N’ wave, and blow-up wave solutions.
- KdV-nKdV equation /
- bifurcation /
- dynamical system /
- trapezoidal wave /
- inverted ‘N’ wave
MSC: 35C07, 34C23, 33E05

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References

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