论文标题
通用的KDV型方程与Boussinesq的方程不均匀 - 数值研究
Generalized KdV-type equations versus Boussinesq's equations for uneven bottom -- numerical study
论文作者
论文摘要
本文的主要目标是比较两种相似但略有不同的方法引起的孤立表面波的运动。在第一种方法中，使用单波方程获得了孤子表面波的数值演变。在第二种方法中，相同初始条件的数值演变是通过对同一Euler方程系统的BousSinesQ方程组的解决方案获得的。我们讨论了小参数$α，β，δ$之间关系的四个与物理相关的情况。对于平底底部，这些情况暗示了Korteweg-de Vries方程（KDV），扩展的KDV（KDV2），第五阶KDV（KDV5）和Gardner方程（GE）。在所有研究的情况下，底部变化对从Boussinesq方程计算出的表面波的幅度和速度的影响要比从单波方程获得的影响要大得多。
The paper's main goal is to compare the motion of solitary surface waves resulting from two similar but slightly different approaches. In the first approach, the numerical evolution of soliton surface waves moving over the uneven bottom is obtained using single wave equations. In the second approach, the numerical evolution of the same initial conditions is obtained by the solution of a coupled set of the Boussinesq equations for the same Euler equations system. We discuss four physically relevant cases of relationships between small parameters $α,β,δ$. For the flat bottom, these cases imply the Korteweg-de Vries equation (KdV), the extended KdV (KdV2), fifth-order KdV (KdV5), and the Gardner equation (GE). In all studied cases, the influence of the bottom variations on the amplitude and velocity of a surface wave calculated from the Boussinesq equations is substantially more significant than that obtained from single wave equations.
