Electron. J. Differential Equations, Vol. 2019 (2019), No. 126, pp. 1-20.

Feng's first-integral method to traveling wave solutions of the Ostrovsky system

Kehua Li, Zhihong Zhao

In this paper, we apply Feng's first-integral method to study traveling wave solutions to a two-component generalization of the Ostrovsky system. We convert the two-component generalization of the Ostrovsky system to an equivalent autonomous system. Then we use the Divisor Theorem of two variables in the complex domain to seek the polynomial first-integral to this autonomous system. Through analyzing the derived first-integral, we obtain traveling wave solutions to the two-component generalization of the Ostrovsky system under certain parametric conditions.

Submitted October 20, 2018. Published November 25, 2019.
Math Subject Classifications: 35C07, 35K40, 35M30.
Key Words: Traveling wave solutions; first-integral; bifurcation; reduced Ostrovsky equation; divisor theorem.

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Kehua Li
School of Applied Mathematics
Xiamen University of Technology
Xiamen, Fujian 361024, China
email: khli@xmut.edu.cn
Zhihong Zhao
School of Mathematics and Physics
University of Science and Technology Beijing
Beijing 100083, China
email: zzh@ustb.edu.cn

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