New computational results for a prototype of an excitable system

Highlights

• The nonlinear predator–prey system for forming new computational results that define a prototype of an excitable system studied using the modified (G'/G)-expansion method.

• We construct many new computational solutions that define hyperbolic, trigonometric, and rational functions.

• The kink-type shape, bright and dark singular lump shape, singular kink shape, and different types of singular kink shapes are retrieved.

• The obtained solutions are presented by 2D, 3D and Contour figures that display the properties of the solutions.

Abstract

This present paper uses a well known computational scheme such as the modified (G'/G)-expansion method to the nonlinear predator–prey (NPP) system for forming new computational results that define a prototype of an excitable system. We construct twenty new computational solutions that define hyperbolic, trigonometric, and rational. Two-dimensional, three-dimensional, and contour shapes are depicted to demonstrate the acquired answers' more physical as well as dynamical features. Comparing our acquired responses and that obtained in previously written research articles presents the novelty of our research. The computational scheme's representation demonstrates its helpful and straightforward procedure that produces a kink-type shape, singular kink shape, bright and dark singular lump shape, multiple bright and dark lump shape, and different types of singular kink shapes. Their ability to manipulate many applications of nonlinear partial differential equations (NLPDEs) is also presented.