Nonlinear Effects

Abstract

Up to this point, we have limited our attention almost exclusively to linear phenomena; that is, to phenomena describable by equations in which the dependent variable occurs to no higher than the first power. The entire treatment of waves in Chapter 4, for instance, depended on the process of linearization, in which higher-order terms were regarded as small and were neglected. This procedure enabled us to consider only one Fourier component at a time, with the secure feeling that any nonsinusoidal wave can be handled simply by adding up the appropriate distribution of Fourier components. This works as long as the wave amplitude is small enough that the linear equations are valid.