利用广义变分迭代方法讨论了一类非线性强迫扰动Klein-Gordon方程.首先，用双曲函数待定系数法求得了无扰动方程孤子波.其次，利用泛函变分迭代原理得到了强迫扰动Klein-Gordon方程的一个摄动近似解.最后，论述了解的一致有效性.得到的近似解是解析式，它可对近似解进行解析运算，这对用简单的模拟方法得到的近似解是达不到的.
In this paper, a class of nonlinear forced disturbed Klein-Gordon equations are considered using the method of generalized variational iteration. Firstly, the solitary waves of an undisturbed Klein-Gordon equation are solved using the method of undetermined coefficients for hyperbolic functions. Then, perturbed approximate solutions for a soliton of a nonlinear forced disturbed Klein-Gordon equation are obtained using the functional variational iterative principle. Finally, the uniform validity for the approximate solutions is proved. The obtained approximate solution is an analytic expression. So it can be used for carrying out analytic operations. However, these cannot be obtained via a simple simulation.
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中国综合性科技类核心期刊(北大核心)