Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

Abstract

In this article, we explore the famous Selkov–Schnakenberg (SS) system of coupled nonlinear partial differential equations (PDEs) for Lie symmetry analysis, self-adjointness, and conservation laws. Moreover, miscellaneous soliton solutions like dark, bright, periodic, rational, Jacobian elliptic function, Weierstrass elliptic function, and hyperbolic solutions of the SS system will be achieved by a well-known technique called sub-ordinary differential equations. All these results are displayed graphically by 3D, 2D, and contour plots.