ABSTRACT
The dynamic properties of media like plasmas can in most relevant cases be described by a set of differential equations, these being linear or nonlinear. This chapter discusses wave propagation in general, with little or no specific reference to plasmas, also with the aim of emphasizing the similarities of wave propagation in various media. A differential equation has to be supplemented with boundary and/or initial conditions. As an alternative to the Cauchy problem, one can choose to prescribe the value of the function at a closed boundary at all times, for instance. In the investigations of, for instance, the Laplace equation, such conditions are discussed and classified in detail. With reference to the special theory of relativity, it is often, but incorrectly, claimed that the group velocity associated with a correctly derived dispersion relation must at all frequencies and wave-numbers be less than the speed of light in vacuum.
