On the Propagation of Dispersive Waves (II)

Abstract

In the present paper, it is explained theoretically that the maximum amplitudes, of a dispersive wave is propagated with maximum, minimum or mini-max group velocities and their magnitudes are O(^-5/6) or O(^-3/4) according as their group velocities are maximum and minimum or mini-max respectively, where ris the distance from the center of region in which the initial displacement or velocity are concentrated.
It is also shown that the wave groups, the indivisual waves of which have the wave length of ∞ or infinitesimal, can not be so predominant as the wave groups above stated even if their group velocities are extremum.
Finally, it is proved that if the initial distribution of displacement or velocity fulfils a certain condition occasionally, the amplitude of wave group with an extremum group velocity may be inferior to those of other wave groups.