PERTURBATION METHOD IN THE SOLUTION OF NONLINEAR STANDING WAVES
微扰法求解非线性驻波问题

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.