非传播孤立波及其相互作用的数值模拟

周显初; 芮燚

非传播孤立波及其相互作用的数值模拟

周显初,
芮燚

中国科学院力学研究所, 北京100080

基金项目: 国家自然科学基金资助项目(19572071);国家基础性研究重大项目《非线性科学》资助项目

详细信息

作者简介:
周显初(1939- ),男,浙江奉化人,研究员.

中图分类号: O353.1
计量
- 文章访问数: 2321
- HTML全文浏览量: 56
- PDF下载量: 553
- 被引次数: 0
出版历程
- 收稿日期: 2000-01-03
- 刊出日期: 2000-12-15

Numerical Simulation of Standing Solitons and Their Interaction

Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P R China

摘要

摘要: 通过数值求解由Miles导出的目前公认的的非传播孤立波的控制方程——一个带复共轭项的非线性立方Schr^Ldinger方程,对非传播孤立波进行研究。讨论了Miles方程中的线性阻尼系数α的值,计算表明,线性阻尼α对形成稳定的非传播孤立波影响很大,Laedke等人关于非传播孤立波的稳定性条件只是一个必要条件,而不是充分条件。模拟了两个非传播孤立波的相互作用,数值模拟表明,两个波的作用模式依赖于系统的参数,对不同的初始扰动及其演化的计算表明,只有适当的初始扰动才能形成单个稳定的非传播孤立波,否则扰动可能消失或发展成多个孤立波。
- 孤立波 /
- 非传播孤立波 /
- 立方Schr^Ldinger方程 /
- 数值模拟
Abstract: Standing soliton was studied by numerical simulation of its governing equation,a cubic Schr^Ldiger equation with a complex conjugate term,which was derived by Miles and was accepted. The value of linear damping in Miles equation was studied.Calculations showed that linear damping effects strongly on the formation of a standing soliton and Laedke&Spatschek stable condition is only a necessary condition,but not a sufficient one.The interaction of two standing solitons was simulated.Simulations showed that the interaction pattern depends on system parameters.Calculations for the different initial condition and its development indicated that a stable standing soliton can be formed only for proper initial disturbance,otherwise the disturbance will disappear or develop into several solitons.
- soliton /
- standing soliton /
- cubic Schr^Ldinger equation /
- numerical simulation

HTML全文

参考文献(14)

[1]	WU Jun-ru, Keolian R, Rudnick I. Observ ation of a no n-propagating hydrodynamic soliton[J]. Phys Rev Lett,1984,52:1421-1424.
[2]	Larraza A, Putterman S. Theory of non-propagating surface-wave solitons[J]. J Fluid Mech,1984,148:443-449.
[3]	Miles J W. Parametrically excited solitary waves[J]. J Fluid Mech,1984,148:451-460.
[4]	Laedke E W, Spatschek K H. On localized solution in nonlin ear Fara day resonance[J]. J Fluid Mech,1991,223:589-601.
[5]	Chen X, Wei R J, Wang B R. Chaos in non-propagating hydrod ynamics solitons[J]. Phys Rev,1996,53:6016-6020.
[6]	Chen W Z, Wei R J, Wang B R. Non-propagating interface solitary wave in fluid[J]. Phys Lett A,1995,208:197-200.
[7]	Chen W Z. Experimental observation of self-localized struc ture in granular material[J]. Phys Lett A,1995,196:321-325.[ZK)
[8]	崔洪农,等. 非传播孤立波的观察及实验结果[J]. 湘潭大学自然科学学报,1986,4:27-34.
[9]	崔洪农,等. 非传播孤立波的特性研究[J]. 水动力学研究与进展,1991,6(1):18-25.
[10]	周显初,崔洪农. 表面张力对非传播孤立波的影响[J]. 中国科学A辑,1992,12:1269-1276.
[11]	周显初. 非传播孤立波和表面张力[J]. 力学学报,1998,30[STBZ (6):672-675.
[12]	颜家壬,黄国翔. 矩形波导中两层流体界面上的非传播孤立波[J]. 物理学报,1998,37:874-880.
[13]	Yan J R, Mei Y P. Interaction between two Wu's solitons[J]. Europhys Lett,1993,23:335-340.
[14]	ZHOU Xian-chu, TANG Shi-min, QIN Su-di. The stability of a standing soliton[A]. In: CHIEN Wei-zang, GUO Zhong-heng, GUO You-zhong Eds. Proc 2nd Int Conf of Nonlinear Mech[C]. Beijing: Peking University Press,1993,455-458.