In fluids dynamics, Korteweg-de Vries-type equations are used to describe certain nonlinear phenomena. This paper studies two modified Korteweg-de Vries equations with non-uniformity terms, which incorporate non-uniformity terms \(\alpha \) and \(\beta \) are arbitrary constants to model soliton dynamics in inhomogeneous fluids. By virtue of the Bell-polynomial approach, bilinear forms of such an equation are obtained. N-soliton solutions are also constructed through the Hirota bilinear method. It can be concluded from this study that the values of c selected in the transformation of the two types of equations is different, but the bilinear expression is the same, from which it can be concluded that the process of solving the soliton solution is the same, but the nature of the solution is different, the equation (1.2) is a soliton solution, and (1.3) is a singular soliton solution. Simultaneously, we present some figures to describe the solitary, the results demonstrate how the parameters \(\alpha \) and \(\beta \) influence wave amplitude decay, phase shift, and velocity. These results provide insight into soliton dynamics in non-uniform media.
