非传播孤立波及其相互作用的数值模拟

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SchrLdinger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。

Numerical Simulation of Standing Solitons and Their Interaction

Standing soliton was studied by numerical simulation of its governing equation,a cubic SchrLdiger 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.