This paper studies the brusselator reaction diffusion model (BRDM) with time- and constantdependent coefficients. The soliton solutions for BRDM with time-dependent coefficients are obtained via
first integral (FIM), ansatz, and sine-Gordon expansion (SGEM) methods. Moreover, it is well known
that stability analysis (SA), symmetry analysis and conservation laws (CLs) give several information for
modelling a system of differential equations (SDE). This is because they can be used for investigating the
internal properties, existence, uniqueness and integrability of different SDE. For this reason, we investigate
the SA via linear stability technique, symmetry analysis and CLs for BRDM with constant-dependent
coefficients in order to extract more physics and information on the governing equation. The constraint
conditions for the existence of the solutions are also examined. The new solutions obtained in this paper
can be useful for describing the concentrations of diffusion problems of the BRDM. It is shown that the
examined dependent coefficients are some of the factors that are affecting the diffusion rate. So, the present
paper provides much motivational information in comparison to the existing results in the literature.