【摘要】 研究在充分低的噪声水平下二维Toom模型中刻画沿着固定界面波动统计性质的一个新奇的三阶非线性偏微分方程,Derrida-Lebowitz-Speer-Spohn方程.首先,获得这个非线性偏微分方程的一个非线性变换,这个非线性变换可以将该方程约化为对应的线性偏微分方程.接着,利用分离变量方法获得了该约化线性偏微分方程的许多显式精确解.最后,借助于这个非线性变换得到原来非线性偏微分方程的丰富的显式精确解.更多还原

【Abstract】 This paper deals with a novel three order nonlinear partial differential equation,the Derrida-Lebowitz-Speer-Spohn equation,which describes the statistical properties of the fluctuations along with an achored interface at a sufficiently low noise level in two-dimensional Toom model. Firstly,a nonlinear transformation of the Derrida-Lebowitz-Speer-Spohn equation is obtained and the Derrida-Lebowitz-Speer-Spohn equation is reduced to a corresponding linear partial differential equation by using this nonlinear transformation. Then many explicit exact solutions for the reduced linear partial differential equation are obtained by applying the method of variable separation. With the aid of the nonlinear transformation given here,abundant explicit exact solutions to the Derrida-Lebowitz-Speer-Spohn equation are obtained in the end.更多还原