Advances in Differential Equations

Bifurcations and exact traveling wave solutions of Gerdjikov-Ivanov equation with perturbation terms

Yuzhen Bai, Yonghui Xia, and Wenjing Zhu

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Abstract

This paper is to find new exact traveling wave solutions of the nonlinear Gerdjikov-Ivanov (for short, GI) equation with perturbation terms. Based on employing the bifurcation theory of planar dynamical systems, we found the exact solutions including periodic wave solution, kink wave solution, anti-kink wave solution and solitary wave solution (bright and dark). Moreover, the explicit expressions of the exact solutions in different parametric domains are given. Finally, we conclude our main results in a theorem at the end of the paper.

Article information

Source
Adv. Differential Equations, Volume 25, Number 5/6 (2020), 279-314.

Dates
First available in Project Euclid: 16 May 2020

Permanent link to this document
https://projecteuclid.org/euclid.ade/1589594420

Mathematical Reviews number (MathSciNet)
MR4099221

Subjects
Primary: 34C23: Bifurcation [See also 37Gxx] 35C07: Traveling wave solutions

Citation

Zhu, Wenjing; Xia, Yonghui; Bai, Yuzhen. Bifurcations and exact traveling wave solutions of Gerdjikov-Ivanov equation with perturbation terms. Adv. Differential Equations 25 (2020), no. 5/6, 279--314. https://projecteuclid.org/euclid.ade/1589594420


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