Modulated Waves

The authors consider a wide and very important class of waves that are referred to as modulated waves - those characterized by a slow variation of the macroscopic parameters of amplitude, frequency and profile. Most of the fundamentals of wave theory may be understood by considering this class of waves. The authors characterize linear and nonlinear wave propagation in terms of a common approach based on slowly varying parameters (modulations). They expand the concept of modulation to include a wide class of wave processes. After examining the nature of waves and wave dispersion, the authors turn to modulated waves in linear dispersive media and then to modulated waves in nonlinear media. Theoretical analysis is supported by examples from different branches of physics: electrodynamics, fluid mechanics, acoustics and the mechanics of solids.