具有局部时间分数阶导数的非线性Zoomeron方程的精确解

New Exact Solutions to the Nonlinear Zoomeron Equation with Local Conformable Time-Fractional Derivative

中文关键词:  分数阶导数  Zoomeron方程  行波解  分支

英文关键词:conformable fractional derivative  Zoomeron equation  traveling wave solution  bifurcation

中文摘要:

      利用R. Khalil所提出的分数阶导数概念,研究具有局部时间分数阶导数的非线性Zoomeron方程,得到该方程行波解所满足方程的相图和分支. 同时运用指数函数展开和首次积分方法,可以得到Zoomeron方程的包括孤立波解、周期解等各类行波解的精确解析表达式.

英文摘要:

      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.