Deformation of bichromatic wave groups based on third order side band solution of Benjamin-Bona-Mahony equation

Abstract

This paper concerns on propagation of Benjamin Bona Mahony (BBM) wave groups. The previous results, experimental, analytical and numerical, show that nonlinear effects will deform wave groups and may lead to large waves with wave heights larger than twice the original input; the deformation may show itself as peaking and splitting. To investigate this, especially at which location the waves will achieve their maximum amplitude, and to determine the amplitude amplification factor, a concept called Maximal Temporal Amplitude (MTA) is applied. This quantity is a tool that can be used to measure the maximum amplitude of the waves over time. In this paper we will use Benjamin-Bona-Mahony (BBM) model and third order side band approximation theory to investigate the peaking and splitting phenomena of the wave groups which is initially in bichromatic signal. The bichromatic signal here is a signal that is described by superposition of two monochromatic signals with the same value in amplitude but slightly different in frequencies. We present that the waves undergo deformation in their propagation.