New travelling wave analytic and residual power series solutions of conformable Caudrey–Dodd–Gibbon–Sawada–Kotera equation

Tariq, Hira; Ahmed, Hijaz; Rezazadeh, Hadi; Javeed, Shumaila; Alimgeer, Khurram Saleem; Nonlaopon, Kamsing; Baili, Jamel; Khedher, Khaled Mohamed

doi:10.1016/j.rinp.2021.104591

Cited by 9 publications

(4 citation statements)

References 56 publications

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“…5 (a–e), 6 (a–e), 7 (a–c). Comparing our results with that have been published in [32] , [33] , [34] , [35] , [36] shows our solutions' novelty, where all our solutions did not have been obtained in those papers. Lastly, the above solutions are put together to figure out how gravity-capillary waves move, how shallow water waves with surface tension move, and how magneto-sound waves interact in plasma.…”

Section: Soliton Solution's Noveltysupporting

confidence: 66%

“…This equation is used to solve complicated issues in solid–state physics, nonlinear optics, plasma physics, fluid dynamics, mathematical biology, nonlinear optics, dislocations in crystals, kink dynamics, chemical kinetics, as well as quantum field theory [31] . Many computational strategies have been successfully employed in the development of various unique soliton wave solutions that provide a more hidden characterization of the shallow water wave [32] , [33] , [34] , [35] , [36] .…”

Section: Introductionmentioning

confidence: 99%

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Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation

Khater

2023

Heliyon

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Section: Soliton Solution's Noveltysupporting

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation

Khater

2023

Heliyon

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“…The RPST has been successfully used to construct the approximate analytic solutions of FDEs without implementing linearization, perturbation, or discretization techniques, showing the reliability and simplicity of this technique. This proposed technique has been successfully applied to investigate the solutions of time-fractional Whitham-Broer-Kaup equations [42], Black-Scholes European option pricing equations [43], the KdV equation [44], the nonlinear Schrödinger equation [45], the Biswas-Milovic equation [46], the Caudrey-Dodd-Gibbon-Sawada-Kotera equation [47], etc. The suggested technique is a reliable, practical, and astonishingly effective tool for examining the approximate solutions of many types of real-life nonlinear models.…”

Section: Introductionmentioning

confidence: 99%

Computational Study for Fiber Bragg Gratings with Dispersive Reflectivity Using Fractional Derivative

Tariq¹,

Akram

Sadaf

et al. 2023

Fractal Fract

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In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cubic–quartic dispersive reflectivity having the Kerr law of nonlinear refractive index structure are retrieved with high accuracy. The residual power series technique is used to derive power series solutions to this model. The fractional derivative is taken in Caputo’s sense. The residual power series technique (RPST) provides the approximate solutions in truncated series form for specified initial conditions. By using three test applications, the efficiency and validity of the employed technique are demonstrated. By considering the suitable values of parameters, the power series solutions are illustrated by sketching 2D, 3D, and contour profiles. The analysis of the obtained results reveals that the RPST is a significant addition to exploring the dynamics of sustainable and smooth optical wave propagation across long distances through optical fibers.

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“…In [11], M-lump and interaction between lumps and kink solitons of the 2D-CDGKSE were studied based on HBM. Novel analytical and numerical solutions of the CDGKSE were established by means of Tanh method and order residual power series method [12]. The HBM was used to obtain some breather wave and lumps solutions to the CDGKSE that was converted into its potential version together with implementing of Cole-Hopf transformation [13].…”

Section: Introductionmentioning

confidence: 99%

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

Abdel‐Gawad

2022

Nonlinear Dyn

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A Generalized (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada equation (2D- gCDGKSE) is an integro-differential equation that describes tow-layer fluid interaction. The non-autonomous (2+1)-dimensional gCDGKSE (NAUT-gCDGKSE) was rarely considered in the literature. In the previous works, the concepts of two-layer fluid interaction and non-uniform fluid were not explored. This motivated us to focus the attention on these themes. Our objective is to inspecting waves structures in non-uniform fluid which describes fluid flows near a solid boundary. Thus, the present work is completely new. Our objective, here, is to inspect waves which are similar to those created in waterfall, water waves behind dams, boat sailing, in the network of canals during water release, and internal waves in submarine. In a uniform fluid, rogue waves occur in open oceans and seas, while in the present case of non-uniform fluid, towering and internal rogue waves occur near barriers (islands) and near submarine, respectively. This was consolidated experimentally, as it was shown that rogue wave is produced in a water tank (which is with solid boundary). The exact solutions of NAUT-gCDGKSE are derived here, by implementing the extended unified method (EUM). In applications, it is found that the EUM is of lower time cost in symbolic computation, than when using Lie symmetry, Darboux and AutoBucklund transformations. The results obtained here are evaluated numerically, and they are displayed in graphs. They reveal multiple waves structures with relevance to waves created near a solid boundary. Among them are towering and internal rogue waves, internal (hollowed) and bulge-U-shape wave and S-shape wave, water fall, saddle wave, and dromoions.

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New travelling wave analytic and residual power series solutions of conformable Caudrey–Dodd–Gibbon–Sawada–Kotera equation

Cited by 9 publications

References 56 publications

Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation

Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation

Computational Study for Fiber Bragg Gratings with Dispersive Reflectivity Using Fractional Derivative

Towering and internal rogue waves induced by two-layer interaction in non-uniform fluid. A 2D non-autonomous gCDGKSE

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