The integrable models have the various applications in the numerous areas of science and engineering. It is an interesting fact to check that these integrable models retain the integrable property while the constant coefficients are replaced by the variable coefficients. In order to investigate such problem, this article considers the variable coefficients well posed nonlinear dynamics Sharma-Tasso-Olver-Burgers equation. The Painlevé analysis technique is implemented to retain the integrable property of the considered equation without any constraints condition on variable coefficients. To derive the analytical solutions, the auto-Bäcklund transformation approach is adopted. The 3D graphs have been drawn for the obtained solutions. These graphs depict the physical behaviour of the equation under consideration in the form of periodic, kink and anti-kink wave surfaces. At last, the Lie symmetry approach is used in order to derive the infinitesimal transformation and point symmetries for this equation.