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.
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