Summary
A class of wave equations, derived by means of a Lagrangian density, is discussed. The dispersion relation W(ω, k)=0, where ω is the frequency and k the wave number of a harmonic wave has been derived and some properties of the functions ω 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.
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References
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Broer, L.J.F., Peletier, L.A. On a class of conservative waves. Appl. sci. Res. 17, 133–149 (1967). https://doi.org/10.1007/BF00419781
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DOI: https://doi.org/10.1007/BF00419781