关于将飞秒脉冲激光用于纳米金属薄膜传导系统的研究

Study of Transfers System for Femtosecond Pulse Laser to Nano Metal Film

本文是利用渐近方法求解一类飞秒脉冲激光纳米金属薄膜传导非线性扰动系统,并讨论该非线性系统对应解的渐近性态.首先,求出了退化问题的解.其次,构造一个泛函,计算它的广义变分,令其变分为零.从而得到了Lagrange乘子.然后利用变分原理,构造出一个广义变分迭代式.因此,可依次求出相应系统解任意次精度的渐近展开式.同时,利用泛函分析变分原理,论述了相应展开式的一致收敛性.并举出了相应的例子,得到了它的渐近解并通过模拟方法给出了其解的曲而图形.通过本文的研究,证实了对纳米金属薄膜传导这类非线性扰动系统的求解方法简单有效,并具有一般意义和广泛的应用前景.

The solution to a class of nonlinear disturbed transfers system for the femtosecond pulse laser to Nano metal lm is obtained by using the asymptotic method. The asymptotic behaviors of corresponding solution to this nonlinear system are discussed. Firstly, the outersolution to the reduced problem is solved. Next, a functional is constructed and its generalizedvariational is calculated, with its variational equivalent to zero. Thus the Lagrange multiplicatoris found. Then, a generalized varitational iteration expansion is constructed by using thevaritational principle. Therefore, arbitrary times of iteration expansions for the correspondingsystem can be solved successively. At the same time, the uniform convergence to the relatedexpansion is accounted by using the variational theory of functional analytic. An example isenumerated, and by using the simulation method, the graphs of surface for its solution are given.From the results obtained in this study, it is validated that the solving method for nonlinear disturbed transfers system to Nano metal lm can be provided in a simple and valid manner by using the generalized variational iteration. And it also has a general theoretical value and a wide application potential.