Nonlinear dynamical wave structures of Zoomeron equation for population models

The nonlinear dynamical exact wave solutions to the non-fractional order and the time-fractional order of the biological population models are achieved for the first time in the framwork of the Paul-Painlevé approach method (PPAM). When the variables appearing in the exact solutions take specific values, the solitary wave solutions will be easily obtained. The realized results prove the efficiency of this technique.