Dynamics of interaction between solitary and rogue wave of the space-time fractional Broer–Kaup models arising in shallow water of harbor and coastal zone

Akter, Selina; Sen, Ratan Kumar; Roshid, Harun-Or

doi:10.1007/s42452-020-03779-8

Cited by 1 publication

(1 citation statement)

References 27 publications

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“…Recently, discoveries of novel explicit and analytical travelling wave solutions of nonlinear models have attracted great attention from blooming scientists [1][2][3]. A series of travelling wave exact solutions with various nonlinear dynamics can be illustrated as unique complex phenomena in diverse scopes of nonlinear sciences, for instance, optics [1][2][3], uid mechanics [4,5], shallow water wave and magneto-sound transmission in plasmas [6], ion-acoustic plasma waves [7,8], shallow water waves [9,10], solid-state physics and chemical kinetics [11], visco-elastic Kelvin Voigt uid [12], shallow water propagation in the harbor and coastal region [13], and nonlinear quantum eld theory [14] . Due to the signi cance of such eld of studies, theoretical probes on physical action emulation of NEEs are sought day by day.…”

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confidence: 99%

Bifurcation Analysis of Travelling Waves and Multi-rogue Wave Solutions for a Nonlinear Pseudo-Parabolic Model of Visco-Elastic Kelvin-Voigt Fluid

Uddin

Karim

Alshammari

et al. 2022

Mathematical Problems in Engineering

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Through this article, we focus on the extension of travelling wave solutions for a prevalent nonlinear pseudo-parabolic physical Oskolkov model for Kevin-Voigt fluids by using two integral techniques. First of all, we explore the bifurcation and phase portraits of the model for different parametric conditions via a dynamical system approach. We derive smooth waves of the bright bell and dark bell, periodic waves, and singular waves of dark and bright cusps, in correspondence to homoclinic, periodic, and open orbits with cusp, respectively. Each orbit of the phase portraits is envisaged through various energy states. Secondly, with the help of a prevalent unified scheme, an inventive version of exact analytic solutions comprising hyperbolic, trigonometric, and rational functions can be invented with some collective parameters. The unified scheme is an excitably auspicious method to procure novel interacting travelling wave solutions and to obtain multipeaked bright and dark solitons, shock waves, bright bell waves with single and double shocks, combo waves of the bright-dark bell and dark-bright bell with a shock, dark bell into a double shock wave, and bright-dark multirogue type wave solutions of the model. The dynamics of the procured nonlinear wave solutions are also presented through 2-D, 3-D, and density plots with specified parameters.

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