Fifth order semi analytical solution of exact Korteweg-de Vries equation

Abstract

Abstract This study concerns on the solution of exact Korteweg de Vries (KdV) equation in its application in generating extreme waves. The method of asymptotic expansion is employed up to the fifth order. In the previous research, the same method was applied up to the third order and fifth order but it only considered the side band solutions. Here, solutions at each order will be analyzed. The existence of resonance terms at the odd orders and side band terms are interesting to observe considering the importance of these quantities in analyzing the wave deformation which link to the phenomenon of wave’s amplitude amplification. Bichromatic signal is used as the initial wave signal as it experiences instability during its propagation which results the amplitude amplification. The amplitude amplification is presented as Maximal Temporal Amplitude (MTA) which is a quantity measuring the highest elevation at every spatial position during the observation time.