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

Abstract

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.

Intensity variability in stationary solutions of the Fractional Nonlinear Schrödinger Equation

“…The NLS equation is an equation that can generally be used to observe the dynamics of waves propagating in a nonlinear dispersive medium, such as Bose-Einstein condensation [12][13], plasma physics [14], double-stranded deoxyribonucleic acid [15], electrical trajectories [16], fluid dynamics [17], and many more. In nonlinear optics, the NLS equation can be used to observe the propagation of electromagnetic waves in a single-mode [17][18][19] optical fiber medium. The NLS equation describes the propagation of electromagnetic waves within an optical fiber that changes slowly.…”

Solutions of Benjamin-Bona-Mahony, modified Camassa-Holm and Degasperis-Procesi equations using an iterative method

“…For more details of DGJM, we refer the reader to a review article [21] and references cited therein. In the present paper, DGJM is used for finding the solutions of the non-linear Benjamin-Mahony equation [22], modified Camassa-Holm and Degasperis-Procesi equations [23].…”

Hydrodynamics and Tidal Turbine Generator Stability Analysis in Several Wave Variations

“…e increase in wave amplitude is greatly influenced by the composition of the wave and its propagation as it moves from the middle of the sea to the land [26][27][28]. As a consequence, the observation of the turbine location takes into account the current strength, as indicated by the water ripples on the surface, as well as the internal current strength [29,30].…”