On a class of conservative waves

A class of wave equations, derived by means of a Lagrangian density, is discussed. The dispersion relation W(, k)=0, where is the frequency and k the wave number of a harmonic wave has been derived and some properties of the functions 2(k 2) have been shown. Conservation laws have been derived, and formal solutions of the initial value problem and a class of mixed initial-boundary value problems have been presented. It has been shown that the solutions of the latter class are causal although the Kramers-Kronig relations are not satisfied.