Abstract <p> This study conducts an approximate symmetry analysis of the singularly Kuramoto–Sivashinsky perturbed version of the modified Gardner equation, renowned for modeling the super-nonlinear propagation of ion–acoustic waves and quantum electron–positron–ion magnetoplasmas, and the Camassa–Holm equation, which serves as a critical model for nonlinear wave dynamics in cylindrical axially symmetric hyperelastic rods. The analysis employs perturbative expansion of infinitesimal generators resulting in the derivation of the approximate infinitesimal generators, which are further systematically utilized in Olver’s optimal theory for constructing an optimal system of Lie subalgebras. Furthermore, elements of the derived system are employed to reduce the governing problems to ordinary differential equations, facilitating the determination of exact invariant solutions by appropriate solution methods. Diverse wave phenomena arise from the intricate interplay of dispersion, nonlinearity, and perturbation effects. Accordingly, graphical depictions of the solutions highlight key nonlinear wave phenomena. </p>