线性Boussinesq方程的色散量子化现象

Dispersion quantization of linear Boussinesq equation

为研究线性Boussinesq方程的周期初边值问题解在大波数条件下的渐近行为,通过将方程解表示成Fourier级数形式,利用Matlab软件进行数值模拟.结果表明:方程色散关系的渐近行为对方程解在大波数条件下的渐近行为起决定性作用,线性Boussinesq方程存在色散量子化现象.

In this paper, we study the asymptotic behavior of solutions to periodic initial boundary value problem for linear Bousssinesq equation with large wave numbers. By expressing the solution of the equation in Fourier series, Matlab is used for numerical simulation. The simulation results show that the asymptotic behavior of the dispersion relation plays a decisive role in the asymptotic behavior of the solution of the equation on the condition of large wave numbers, which indicates that the dispersion quantization phenomenon exists in the linear Bousenisq equation.