Novel dynamics of wave solutions for Cahn–Allen and diffusive predator–prey models using MSE scheme

Abstract

Abstract By employing modified simple equation (MSE) scheme, we estimate the presence of stable kink soliton and kinky-periodic rogue wave solutions; unstable singular kink wave solutions of the biological dynamical models as a Cahn–Allen model and a diffusive predator–prey model. This model frequently occurs in various nonlinear science including quantum physics, plasmas and biophysics. We present some novel exact explicit solutions of the exponential form of both Cahn–Allen and diffusive predator–prey models with some free parametric values. We also derive particular solutions from the explicit solutions selecting some definite values of the free parametric values. As a result, kink, singular kink and kinky-periodic lump wave surfaces are achieved of the solutions. Lastly, the variety and graphic representations of the composition make the models dynamic. Stable and unstable situations are explained in detail from the analysis of the profiles.