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