消除Padé数值格式中人工耗散引起的拖尾和延迟以实现稳定的紧致孤子碰撞
Removing trailing tails and delays induced by artificial dissipation in Padé numerical schemes for stable compacton collisions
AI总结：
针对Rosenau-Hyman K(n,n)方程的紧致孤子碰撞数值模拟，通过绝热扰动方法平衡两种人工耗散源，在Padé格式中消除拖尾、振幅衰减和延迟，同时保持数值稳定性。
摘要：
由Rosenau-Hyman K(n,n)方程产生的具有紧支撑的碰撞孤立波的数值模拟，在大多数方法中需要添加人工耗散以保证稳定性。代价是随着解的演化出现拖尾、振幅衰减和延迟。这些不良效应可以通过适当平衡两种人工耗散源来校正；该过程利用绝热扰动方法确定的耗散下孤立波参数的慢时间演化来设计。在Padé数值格式上证明了拖尾去除方法的有效性。拖尾被完全消除，仅在其前沿原始位置留下一个小而紧凑的涟漪，并且格式在紧致孤子碰撞下的数值稳定性得以保持，如对多个n值的大量数值实验所示。
英文摘要：
The numerical simulation of colliding solitary waves with compact support arising from the Rosenau-Hyman K(n,n) equation requires the addition of artificial dissipation for stability in the majority of methods. The price to pay is the appearance of trailing tails, amplitude damping, and delays as the solution evolves. These undesirable effects can be corrected by properly counterbalancing two sources of artificial dissipation; this procedure is designed by using the slow time evolution of the parameters of the solitary waves under the presence of the dissipation determined by means of adiabatic perturbation methods. The validity of the tail removal methodology is demonstrated on a Padé numerical scheme. The tails are completely removed leaving only a small compact ripple at the original position of their front, and the numerical stability of the scheme under compacton collisions is preserved, as shown by extensive numerical experiments for several values of n.
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