This article discusses the evolution of Benjamin-Bona-Mahony (BBM) wave packet�s envelope.The envelope equation is derived\nby applying the asymptotic series up to the third order and choosing appropriate fast-to-slow variable transformations which\neliminate the resonance terms that occurred. It is obtained that the envelope evolves satisfying the Nonlinear Schrodinger (NLS)\nequation. The evolution of NLS envelope is investigated through its exact solution, Soliton on Finite Background, which undergoes\nmodulational instability during its propagation. The resulting wave may experience phase singularity indicated by wave splitting\nand merging and causing amplification on its amplitude. Some parameter values take part in triggering this phenomenon. The\namplitude amplification can be analyzed by employing Maximal Temporal Amplitude (MTA) which is a quantity measuring the\nmaximum wave elevation at each spatial position during the observation time.Wavenumber value affects the extreme position of\nthe wave but not the amplitude amplification. Meanwhile, modulational frequency value affects both terms. Comparison of the\nevolution of the BBM wave packet to the previous results obtained from KdV equation gives interesting outputs regarding the\nextreme position and the maximum wave peaking.
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