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

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.