Some properties of the solutions of wave equations

L.J.F. Broer, L.A. Peletier

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)


Some properties of solutions of initial value problems and mixed initial-boundary value problems of a class of wave equations are discussed. Wave modes are defined and it is shown that for the given class of wave equations there is a one to one correspondence with the roots i (k) or k j () of the dispersion relation W(, k)=0. It is shown that solutions of initial value problems cannot consist of single wave modes if the initial values belong to W 2 1 (–, ); generally such solutions must contain all possible modes. Similar results hold for solutions of mixed initial-boundary value problems. It is found that such solutions are stable, even if some of the singularities of the functions k j () lie in the upper half of the plane. The implications of this result for the Kramers-Kronig relations are discussed.
Original languageEnglish
Pages (from-to)138-161
JournalApplied Scientific Research
Issue number1
Publication statusPublished - 1969


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