Solitary waves of the equal width wave equation
Solitary waves of the equal width wave equation
复制标题
等宽波动方程的孤立波
DOI：
10.1016/0021-9991(92)90054-3
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
G. A. Gardner
中科院分区：
文献类型：
--
作者：
L. Gardner;G. A. Gardner
本文用三次B样条有限元Galerkin法数值求解等宽波动方程，模拟孤立波的迁移和相互作用。两个孤立波的相互作用被认为是造成孤立波源的创建。通常这些波的振幅很小，但当两个相互作用的波的振幅相等且方向相反时，源产生孤立波列，其振幅与初始波的振幅在同一数量级。的运动的三个不变量进行评估，以确定系统的守恒性质。最后，研究了麦克斯韦初始脉冲的时间演化。对于小δ（Ut+UUx−δUxxt=0），只形成正波，其行为与KdV和FILW方程相似。对于较大的d值，产生正和负孤立波。
A numerical solution of the equal width wave equation, based on Galerkin's method using cubic B-spline finite elements is used to simulate the migration and interaction of solitary waves. The interaction of two solitary waves is seen to cause the creation of a source for solitary waves. Usually these are of small magnitude, but when the amplitudes of the two interacting waves are equal and opposite the source produces trains of solitary waves whose amplitudes are of the same order as those of the initiating waves. The three invariants of the motion are evaluated to determine the conservation properties of the system. Finally, the temporal evolution of a Maxwellian initial pulse is studied. For small δ (Ut+UUx−δUxxt=0) only positive waves are formed and the behaviour mimics that of the KdV and FILW equations. For larger values of d both positive and negative solitary waves are generated.