An Envelope Equation of Benjamin-Bona-Mahony Wave Group

Halfiani, Vera; Salmawaty,; Ramli, Marwan

doi:10.17654/ms102061077

Cited by 4 publications

(7 citation statements)

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“…KdV wave packet with its NLS envelope has been applied to study the occurrence of extreme waves in many areas, not only in the fluid dynamic but also in the fields of plasma physics, quantum electronic, and optics [41][42][43][44][45]. BBM wave packet envelope had been also analyzed in [46]. The study found that envelope evolves satisfying the NLS equation.…”

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

“…In the next section, we will briefly review the BBM wave packet envelope which is adopted from the study in [46]. Also we will derive the elevation equation based on the wave packet and the obtained envelope equation.…”

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

“…The derivation of NLS equation from BBM equation can be thoroughly studied in [46]. NLS equation has many solutions.…”

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Evolution of Benjamin-Bona-Mahony Wave Packet due to an Instability of a Pair of Modulations

Halfiani

Fadhiliani

Mardi

et al. 2018

International Journal of Differential Equations

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

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Section: International Journal Of Differential Equationsmentioning

confidence: 99%

Section: International Journal Of Differential Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Evolution of Benjamin-Bona-Mahony Wave Packet due to an Instability of a Pair of Modulations

Halfiani

Fadhiliani

Mardi

et al. 2018

International Journal of Differential Equations

Self Cite

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show abstract

“…A similar method was applied in [68] to study the phase singularity of the wave group BBM equation. By obtaining the NLS envelope, Halfiani et al [69] show that the wave profile occurs separation and unification of waves around extreme waves.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the wave criteria for extreme wave generation in the laboratory are sufficient. Moreover, it is known that the waveform of BBM meets the Nonlinear Schrodinger equation [69]. This NLS equation has different nonlinear and dispersion coefficients with the NLS envelope of the KdV waveform.…”

Section: Introductionmentioning

confidence: 99%

The dynamics of surface wave propagation based on the Benjamin Bona Mahony equation

Fadhiliani

Halfiani

Ikhwan

et al. 2020

Heliyon

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Modulation instability is one of the consequences of the water medium's inclination. It causes surface water waves to run into phenomena of splitting and merging in their propagation. An increase in wave amplitude follows this phenomenon, which can encourage the appearance of extreme waves. It is known that the Benjamin Bona Mahony (BBM) wave has modulation instability in its propagation, with the envelope evolving by the equation Nonlinear Schrodinger (NLS) equation dynamic. One of the NLS equation solution is known as Soliton on Finite Background (SFB). SFB is a continuation of the Benjamin-Feir nonlinear terms. Here, the probe of the BBM wave dynamics is conducted by transforming the complex amplitudes form of SFB variable into the polar form of displaced phase-amplitude. It was done to observe changes in the amplitude of the wave in a complex plane with phases that depend only on position. The description of the dynamics of the SFB can be illustrated through Argand diagrams. It was found that the modulation frequency affects the SFB phase: the smaller the modulation frequency, the higher the phase angle. Also, it is found that the phenomenon of SFB phase singularity occurs in extreme waves for certain frequency modulation intervals.

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Soliton solution of Benjamin-Bona-Mahony equation and modified regularized long wave equation

Ramli

Irsalina

Iwanisa

et al. 2017

AIP Conference Proceedings

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An Envelope Equation of Benjamin-Bona-Mahony Wave Group

Cited by 4 publications

References 0 publications

Nonlinear Evolution of Benjamin-Bona-Mahony Wave Packet due to an Instability of a Pair of Modulations

Nonlinear Evolution of Benjamin-Bona-Mahony Wave Packet due to an Instability of a Pair of Modulations

The dynamics of surface wave propagation based on the Benjamin Bona Mahony equation

Soliton solution of Benjamin-Bona-Mahony equation and modified regularized long wave equation

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