一类非线性广义强阻尼时滞扰动Sine-Gordon方程初值问题

A Class of Nonlinear Generalized Strong Damping Time Delay Disturbed Sine-Gordon Equation Initial Value Problem

本文讨论了一类非线性广义Sine-Gordon扰动方程,基于渐近理论得到对应方程的时滞初值问题并求出渐近解析解.首先,利用Fourier变换方法得出外部解.其次,按时滞变量展开扰动函数,再根据摄动方法和理论求出强阻尼时滞扰动广义SineGordon方程初值问题的的渐近解.根据本文的理论和方法得到的渐近解是解析的表示式,能够进行解析运算,从而可得到相关的物理量的性状,扩大了问题的讨论范围.

In this paper, a class of nonlinear generalized Sine-Gordon disturbed equation is considered. From the asymptotic theory, the asymptotic analytic solution to corresponding equation time delay initial value problem is solved. Firstly, the outer solution is found by using the Fourier transform method. Secondly, the disturbed function is developed from the time delay variable. Then, the uniformly valid solution to the strong damping time delay disturbed generalized Sine-Gordon equation initial value problem is obtained by the perturbation method and theory. Moreover, the asymptotic solution is an analytic expansion, and able to do analytic operation. Therefore, the corresponding physical characters are derived, and application ?elds are enlarged.