New Exact Solutions to the Nonlinear Zoomeron Equation with Local Conformable Time-Fractional Derivative
Received:February 07, 2019  Revised:September 04, 2019
Key Word: conformable fractional derivative   Zoomeron equation   traveling wave solution   bifurcation
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11301006) and the Natural Science Foundation of Anhui Province (Grant No.1408085MA01).
 Author Name Affiliation Chunlei HE School of Mathematics and Statistics, Anhui Normal University, Anhui 241002, P. R. China Shoujun HUANG School of Mathematics and Statistics, Anhui Normal University, Anhui 241002, P. R. China Chunping XIA School of Mathematics and Statistics, Anhui Normal University, Anhui 241002, P. R. China Yangyang XU School of Mathematics and Statistics, Anhui Normal University, Anhui 241002, P. R. China
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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. 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.