非传播孤立波及其相互作用的数值模拟  

Numerical Simulation of Standing Solitons and Their Interaction

作　　者：周显初[1] 芮燚 

机构地区：[1]中国科学院力学研究所,北京100080

出　　处：《应用数学和力学》2000年第12期1238-1246,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目! ( 19572 0 71);国家基础性研究重大项目!<非线性科学>资助项目

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 dinger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 。Standing soliton was studied by numerical simulation of its governing equation, a cubic Schrdiger 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.

关 键 词：非传播弧立波 数值模拟 相互作用 立方薛定谔方程 

分 类 号：O353.1[理学—流体力学]