Nonlinear evolution of bichromatic waves based on the fifth order solution of benjamin bona mahony equation

Abstract

This research concerns on the influence of higher order solution to nonlinear evolution of bichromatic waves based on Benjamin Bona Mahony (BBM) equation. Asymptotic method was applied to determine the solution expanded to the fifth order. In previous researches, this method was applied on the same equation to find its solution up to the third order and it was obtained that the waves underwent deformation and amplitude amplification affected by the occurrence of a pair of side bands during their propagation. In this study, the effect of the higher order solution on the increasing amplitude was observed. A quantity called as Maximal Temporal Amplitude (MTA) was measured to find the maximum position where the highest amplitude occurred and the Amplitude Amplification Factor (AAF). MTA gives information about the waves’ highest elevation at every spatial position during the observation time. The analysis includes comparison between the third and fifth order solutions in their contribution to the rise of the amplitude and the maximum position.