Plenty accurate soliton wave solutions of the prototype of an excitable system

Abstract

In this paper, the nonlinear fractional Lotka–Volterra model is analyzed and numerically studied. This research is based on applying the three latest analytical schemes and three other numerical schemes to construct rich wave solutions. In different forms, many novel solitary wave solutions are built and presented in two-dimensional, three-dimensional, and contour plots. The numerical method conditions are evaluated through the obtained analytical solutions, and the accuracy of the analytical solutions is studied. Many numerical solutions are constructed based on the employed schemes. Additionally, the analytical, semi-analytical, numerical, and absolute values of error between the values of obtained solutions are calculated with the different values of the given variable in the solutions. Furthermore, the match between the obtained analytical solution and the numerical solution has been explained through some two-dimensional distributed radar charts. The contribution of this article is demonstrated by comparing the obtained solution with the recently published results of the same model.