Spatio-temporal dynamic solitary wave solutions and diffusion effects to the nonlinear diffusive predator-prey system and the diffusion-reaction equations

The coupled parabolic nonlinear evolution equations that describe the temporal-spatio dynamics of predator prey systems and the nonlinear diffusion-reaction equations with diffusion effects have broad applications in biology, population dynamics, ecology, and many other fields where nonlinearity and diffusivity are key features of wave evolution. As a result, exact traveling wave solutions of such models are highly effective in numerical and analytical theories. In this article, we find the soliton solutions of the above stated biological models by contriving the enhanced modified simple equation method which is related to the exponential, hyperbolic, and trigonometric functions by balancing the highest order nonlinearity and diffusivity associated with biological groups. Graphical representations of some of the obtained solutions in three-and two-dimensional layouts are provided to estimate their behavior. The results revealed that the stated method is categorical, robust, and efficient in finding exact solutions to a variety of nonlinear evolution equations.(c) 2022 Elsevier Ltd. All rights reserved.