SOLITARY WAVE INTERACTIONS OF THE GRLW EQUATION
SOLITARY WAVE INTERACTIONS OF THE GRLW EQUATION
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DOI：
10.1016/j.chaos.2006.01.016
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发表时间：
2007-07
影响因子：
7.8
通讯作者：
J. Ramos
中科院分区：
文献类型：
--
作者：
J. Ramos
提出了一种基于时间和空间导数分离的三点四阶精度紧致差分方程组的广义正则化长波(GRLW)方程的近似拟线性化方法。该方法建立了一个具有三对角矩阵的线性方程组，并用于确定GRLW方程的参数和初始条件对波动孔形成和两个孤立波之间相互作用/碰撞的影响。结果表明，该方法非常准确地保留了GRLW方程的前两个不变量，二次波的形成是初始高斯条件的幅度和宽度的强函数，两孤立波之间的碰撞是GRLW方程中出现的参数和初始条件的幅度和速度的强函数。结果还表明，前、尾波的陡化可能会形成多个二次波和/或波浪形涌浪，前者与尾随孤立波相互作用，后者可能平行于或会聚到前孤立波。
An approximate quasilinearization method for the solution of the generalized regularized long-wave (GRLW) equation based on the separation of the temporal and spatial derivatives, three-point, fourth-order accurate, compact difference equations, is presented. The method results in a system of linear equations with tridiagonal matrices, and is applied to determine the effects of the parameters of the GRLW equation and initial conditions on the formation of undular bores and interactions/collisions between two solitary waves. It is shown that the method preserves very accurately the first two invariants of the GRLW equation, the formation of secondary waves is a strong function of the amplitude and width of the initial Gaussian conditions, and the collision between two solitary waves is a strong function of the parameters that appear in the GRLW equation and the amplitude and speed of the initial conditions. It is also shown that the steepening of the leading and trailing waves may result in the formation of multiple secondary waves and/or an undular bore; the former interacts with the trailing solitary wave which may move parallel to or converge onto the leading solitary wave.