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摘要: 在历史上,用微扰法求解非线性驻波是不成功的。本文对此进行了分析,认为微扰法给出的一次解是基本解,决定了驻波的基本波形。二次以上的解是由于非线性对波形的影响,使驻波波形上各点随时间运动稍加变动,因此对二次以上的微量只应保留其时间微商。这样所得解不但是稳定的,并且与根据波动方程的严格解基本相同。
Abstract: In the history, perturbation method was unsuccessful in the solution of nonlinear standing waves. This problem is reviewed. It is apparent that the first order solution of the wave equation for standing wave by the perturbation method gives the basic solution, determining the basic wave form of the standing wave. The second and higher order solutions modify the time - dependent motion of the particle at different points on the wave form due to the nonlinearity, and hence only the time derivatives of the higher order quantities should be preserved. The results thus obtained are stable and essentially agree to the exact solution of the wave equation.