New exact solutions to the nonlinear Zoomeron equation with local conformable time-fractional derivative
Received:February 07, 2019  Revised:June 15, 2019
Key Word: Conformable fractional derivative   Zoomeron equation   Traveling wave solution   Bifurcation.
Fund ProjectL:National Natural Science Foundation of China (Grant No. 11301006; the Anhui Provincial Natural Science Foundation (Grant No. 1408085MA01)
 Author Name Affiliation E-mail Chunlei He Anhui Normal University clhe@ahnu.edu.cn Shoujun Huang Anhui Normal University sjhuang@ahnu.edu.cn Chunping Xia Anhui Normal University Yangyang Xu Anhui Normal University
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In this paper, we are concerned with the nonlinear Zoomeron equation with local conformable time-fractional derivative. The concept of local conformable fractional derivative was newly proposed by R. Khalil et al [14]. The bifurcation and phase portrait analysis of traveling wave solutions of the nonlinear Zoomeron equation are investigated. Moreover, by utilizing the $\text{exp}(-\phi(\varepsilon))$-expansion method and the first integral method, we obtained various exact analytical traveling wave solutions to the Zoomeron equation such as solitary wave, breaking wave and periodic wave.