An approach to linear and non-linear wave coupling using dispersion and energy relations †

Abstract

By inclusion of an. external driving force, wave motion of any kind can be characterized by a dispersion function. This function is closely related to the energetic properties of wave motion, and then also to the averaged Lagrangian density. Linear and nonlinear wave interaction can be analysed by inclusion of internal driving forces. Normalization procedures for the amplitudes can be avoided and time and space perturbations studied simultaneously. This analysis is further connected to slowly varying amplitudes and quasi-monochromatic waves. This paper presents the above-mentioned method and applies it to linear two-wave coupling, and non-linear three-wave coupling between positive and negative energy waves, and finally to amplitude modulation. The general equations obtained by this procedure are useful for general discussions. The simplicity of the method may prove useful in different applications.