Abstract:
Abstract: To deeply understand the characteristics of a class of fourth - order nonlinear thin - film equations and to reveal the evolutionary behavior of their solutions, exact solutions of the equations were derived. The conditional Lie - Bäcklund symmetry was adopted for symmetry analysis and reduction, and the generalized separation variable solutions of the equations were obtained. Maple software was used for symbolic computation and numerical solutions, and MATLAB software was utilized to realize the visual representation of the solutions. The exact solutions of the equations were obtained, and the corresponding two - dimensional and three - dimensional graphs were plotted, which intuitively showed the dynamic behaviors and evolutionary characteristics of the solutions. The obtained exact solutions can accurately describe the evolutionary laws of the fourth - order nonlinear thin - film equations, aiming to provide a reference for the further research of this type of equations.