Perturbation technique in theory of nonlinear standing waves

Perturbation teclmique has been disused in the theory of nonlinear standing waves for tens of years, with consequence of questionable, unstable results. The reason is that these earlier authors did not stick to the fundamental properties of standing waves in their mathematical treatments. Stable solutions result,agreeing with the exact theory of nonlinear standing waves, once the standing wave viewpoint is stressed throughout the derivation. This suggests that principles of physics must be used to direct the mathematical manipulation closely in solving a problem of physics.