MAXIMAL TEMPORAL AMPLITUDE (MTA) OF TRI-CHROMATIC SIGNALS

Abstract

Previous numerical and experimental results about surface waves which
are originally bi-chromatic signal on the wave maker, show
phenomenon about peaking and splitting dwing their propagation in the
wave tank. To investigate this phenomenon, especially in peaking, a
quantity called Maximal Temporal Amplitude (MTA) is introduced.
This quantity can be used to predict the position of the occurrence of
maximal peaking. ln this paper, we present the MTA form of tricluomatic
signal, especially to predict the position of maximal peaking
of the signal. Here, the tri-chromatic signal is a superposition of three
mono-chromatic signals with different of amplitudes, frequencies and
initial phases. We use KdV equation with exact dispersion relation
(linear) as a model. We get some approximated solution by expanding
the equation in the power series of amplitude and wave number of trichromatic
signal up to third order.

Keywords : Phase tri-chromatic signal, Maximal Temporal Amplitude