Nonlinear evolution of Benjamin-Feir wave group based on third order solution of Benjamin-Bona-Mahony equation

4th International Conference on Operational Research

Zahnur^1,2 ; Halfiani, Vera^3 ; Salmawaty^4 ; Tulus^5 ; Ramli, Marwan^3,4

University of Sumatera Utara, Indonesia^1

Department of Informatics, Syiah Kuala University, Banda Aceh

23111, Indonesia^2

Dynamic Application and Optimization Research Group, Syiah Kuala University, Banda Aceh

23111, Indonesia^3

Department of Mathematics, Syiah Kuala University, Banda Aceh

23111, Indonesia^4

Department of Mathematics, University of Sumatra Utara, Medan

20155, Indonesia^5

关键词: Benjamin-Bona-mahony equation;    Maximum amplitude;    Nonlinear effect;    Nonlinear evolutions;    Side bands;    Third order;    Wave amplitudes;    Wave deformations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/300/1/012043/pdf
DOI  :  10.1088/1757-899X/300/1/012043

来源: IOP

【 摘 要 】

This study concerns on the evolution of trichromatic wave group. It has been known that the trichromatic wave group undergoes an instability during its propagation, which results wave deformation and amplification on the waves amplitude. The previous results on the KdV wave group showed that the nonlinear effect will deform the wave and lead to large wave whose amplitude is higher than the initial input. In this study we consider the Benjamin-Bona-Mahony equation and the theory of third order side band approximation to investigate the peaking and splitting phenomena of the wave groups which is initially in trichromatic signal. The wave amplitude amplification and the maximum position will be observed through a quantity called Maximal Temporal Amplitude (MTA) which measures the maximum amplitude of the waves over time.