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 exp(-■(ε))-expansion method and the rst integral method,we obtained various exact analytical traveling wave solutions to the Zoomeron equation such as solitary wave,breaking wave and periodic wave.
This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.
