一类四阶非线性薄膜方程的对称约化及数值模拟

Numerical simulation and symmetry reduction for a class of fourth-order nonlinear thin-film equation

  • 摘要: 为深入理解一类四阶非线性薄膜方程的特性,并揭示其解的变化规律,求解了其精确解.采用条件Lie-Bäcklund对称进行了对称分析与约化,获得了方程的广义分离变量解;运用Maple软件进行了符号计算及数值求解,并利用MATLAB软件实现了解的可视化表达,得到了该方程的精确解,并绘制了相应的二维图和三维图,直观展现了解的动态行为与变化特征.通过所得的精确解可准确描述四阶非线性薄膜方程的变化规律,以期为该类方程的进一步研究提供参考.

     

    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.

     

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