A study on the solutions of (1+1)-dimensional Mikhailov-Novikov-Wang equation

Demiray, Şeyma Tülüce; BAYRAKCI, Uğur

doi:10.53391/mmnsa.2022.021

Cited by 4 publications

(5 citation statements)

References 22 publications

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“…Hence, we have proved that c i (x, τ) is a Cauchy sequence in Banach space. erefore, the series solution given in (15) converges towards the solution of (5).…”

Section: Complexitymentioning

confidence: 92%

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Soliton Solutions of Generalized Third Order Time‐Fractional KdV Models Using Extended He‐Laplace Algorithm

et al. 2022

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In this research, the He-Laplace algorithm is extended to generalized third order, time-fractional, Korteweg-de Vries (KdV) models. In this algorithm, the Laplace transform is hybrid with homotopy perturbation and extended to highly nonlinear fractional KdVs, including potential and Burgers KdV models. Time-fractional derivatives are taken in Caputo sense throughout the manuscript. Convergence and error estimation are confirmed theoretically as well as numerically for the current model. Numerical convergence and error analysis is also performed by computing residual errors in the entire fractional domain. Graphical illustrations show the effect of fractional parameter on the solution as 2D and 3D plots. Analysis reveals that the He-Laplace algorithm is an efficient approach for time-fractional models and can be used for other families of equations.

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“…Hence, we have proved that c i (x, τ) is a Cauchy sequence in Banach space. erefore, the series solution given in (15) converges towards the solution of (5).…”

Section: Complexitymentioning

confidence: 92%

“…Solitary wave equations like (1 + 1)-dimensional Mikhailov-Novikov-Wang equation (15), RLW equation (16), complex Ginzburg-Landau model [17], and Korteweg and de Vries equations [18] have assembled a lot of interest from researchers. Among them, the most relevant family is KdV equations which also provide a foundation for other models.…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions of Generalized Third Order Time‐Fractional KdV Models Using Extended He‐Laplace Algorithm

et al. 2022

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“…Nonlinear wave phenomena are studied in a wide range of scientific and engineering fields, such as optical fibers, computational fluid dynamics, plasma physics, solid-state physics chemical dynamics, biological, and chemical-physical science, geochemistry, and shallow waves [4][5][6]. Nonlinear wave processes involving dissipation, dispersion, responses, convection, and propagation are crucial in understanding nonlinear wave equations [7][8][9]. Many approaches have been applied in recent years to examine nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

Usman,

Hussain,

Ali

et al. 2024

International Journal of Mathematics and Computer in Engineering

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This study delves into the exploration of three distinct envelope solitons within the nonlinear dispersive modified Benjamin Bona Mahony (NDMBBM) equation, originating from seismic sea waves, and the Kudryashov-Sinelshchikov (KS) equation. The solitons emerge naturally during the derivation process, and their existence is scrutinized using the ansatz approach. The findings reveal the presence of non-topological (bright), topological (dark) solitons, and rogue wave (singular) solitons, presenting significant applications in applied research and engineering. Additionally, two-dimensional and three-dimensional revolution plots are employed with varying parameter values to scrutinize the physical characteristics of these solitons.

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“…In this paper, we aim to find the exact analytical solution of the MNW equation using a unified method. We consider MNW equation [34][35][36][37], which can be expressed as follows,…”

Section: Introductionmentioning

confidence: 99%

Dynamic nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang equation using the unified approach

Kumar,

Kumar

2023

International Journal of Mathematics and Computer in Engineering

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In this work, we investigate the dynamical study of the (1+1)-dimensional Mikhailov-Novikov-Wang (MNW) equation via the unified method is investigated. This technique is used to obtain the soliton solutions, including the trigonometric function solution, the periodic function solution, the exponential function solution, the elliptic function solution, and other soliton-form solutions. All the obtained results in this work utilizing an effective unified method help gain a better understanding of the physical meaning and behavior of the equation, thus sheding light on the significance of investigating diverse nonlinear wave phenomena in physics and ocean engineering. These derived results are entirely new and never repeated in the previous works done by the other authors. For the interest of visual presentation and physical illustrations, we plot the graphical demonstrations of some of the specified solutions in 3-dimensional, contour, and 2-dimensional plots by using Mathematica software. Consequently, we observe that the acquired solutions of the MNW equations are anti-bell-shape, kink wave solution, solitary wave, periodic solution, multisoliton, and different types of soliton solutions.

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A study on the solutions of (1+1)-dimensional Mikhailov-Novikov-Wang equation

Cited by 4 publications

References 22 publications

Soliton Solutions of Generalized Third Order Time‐Fractional KdV Models Using Extended He‐Laplace Algorithm

Soliton Solutions of Generalized Third Order Time‐Fractional KdV Models Using Extended He‐Laplace Algorithm

Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

Dynamic nature of analytical soliton solutions of the (1+1)-dimensional Mikhailov-Novikov-Wang equation using the unified approach

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