A Study of the Wave Dynamics for the Reaction‐Diffusion Brusselator System and RKL Equation

In this article, the reaction‐diffusion Brusselator system and the Radhakrishnan, Kundu, and Laskshmanan (RKL) equation are discussed. The investigation is focused on the solution procedure of the nonlinear evolution equations in chemical and biological processes. Two approaches, namely the tan( θ /2)‐expansion approach and the exp(−Ω( η ))‐expansion approach, are considered. A multitude of precise solutions is derived for the aforementioned equation. The phase portraits are generated using the Maple program by specifying predefined parameters. The solutions of the stated equations include the tan‐expansion function solutions, the kink solitary wave solutions, and the solitary wave solutions. The obtained results using both methods are useful and constructive and also are reliable for solving nonlinear partial differential equations used in nonlinear sciences.