Solitary waves of the EW and RLW equations
Solitary waves of the EW and RLW equations
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DOI：
10.1016/j.chaos.2006.04.015
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发表时间：
2007-12
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
采用八种有限差分方法来研究等宽（EW）和正则化长波（RLW）方程的孤立波。这些方法包括二阶精确（空间）隐式和线性隐式技术、三点四阶精确紧凑算子算法、基于线性二阶常微分方程局部积分的指数方法以及一阶和二阶精确时间离散化。结果表明，当精确解可用时，针对 EW 和 RLW 方程的三个不变量以及 L2 范数误差进行评估，采用 Crank-Nicolson 离散化的紧凑算子方法比其他七种技术更准确。还表明，根据高斯初始条件的幅度和宽度，使用高斯初始条件可能会导致 EW 方程形成正或负的二次孤立波，以及 RLW 方程形成带或不带振荡尾部的正孤立波。在任何一种情况下，都表明次级波的产生可能先于初始条件的陡化和变窄。据报道，次级波的产生也发生在耗散 RLW 方程中，而 EW 方程中的耗散效应的特征是孤立波的振幅减小、宽度增加和轨迹弯曲。 EW 和 RLW 方程的孤立波的碰撞和发散也根据波幅和这些方程的不变量来考虑。
Eight finite difference methods are employed to study the solitary waves of the equal-width (EW) and regularized long–wave (RLW) equations. The methods include second-order accurate (in space) implicit and linearly implicit techniques, a three-point, fourth-order accurate, compact operator algorithm, an exponential method based on the local integration of linear, second-order ordinary differential equations, and first- and second-order accurate temporal discretizations. It is shown that the compact operator method with a Crank–Nicolson discretization is more accurate than the other seven techniques as assessed for the three invariants of the EW and RLW equations and the L2-norm errors when the exact solution is available. It is also shown that the use of Gaussian initial conditions may result in the formation of either positive or negative secondary solitary waves for the EW equation and the formation of positive solitary waves with or without oscillating tails for the RLW equation depending on the amplitude and width of the Gaussian initial conditions. In either case, it is shown that the creation of the secondary wave may be preceded by a steepening and an narrowing of the initial condition. The creation of a secondary wave is reported to also occur in the dissipative RLW equation, whereas the effects of dissipation in the EW equation are characterized by a decrease in amplitude, an increase of the width and a curving of the trajectory of the solitary wave. The collision and divergence of solitary waves of the EW and RLW equations are also considered in terms of the wave amplitude and the invariants of these equations.