Solitons and lump wave solutions to the graphene thermophoretic motion system with a variable heat transmission

Arif, Adeel; Younis, Muhammad; Imran, Muhammad; Tantawy, M.; Rizvi, Syed T. R.

doi:10.1140/epjp/i2019-12679-9

Cited by 42 publications

(18 citation statements)

References 20 publications

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“…The nonlinear partial differential equation is a physical and natural model which can be used for model constructs by scientists and researchers. Different types of differential equations of both ODEs and PDEs in various fields of science, like fluid flow, mechanics, and biology, are expressed in the special forms [1,2]. There is no particular method for accessing the exact type solutions of nonlinear PDEs but some approximate and analytical solutions have been determined [3,4].…”

Section: Introductionmentioning

confidence: 99%

Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics

et al. 2021

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The Hirota bilinear method is employed for searching the localized waves, lump–solitons, and solutions between lumps and rogue waves for the fractional generalized Calogero–Bogoyavlensky–Schiff–Bogoyavlensky–Konopelchenko (CBS-BK) equation. We probe three cases including lump (combination of two positive functions as polynomial), lump–kink (combination of two positive functions as polynomial and exponential function) called the interaction between a lump and one line soliton, and lump–soliton (combination of two positive functions as polynomial and hyperbolic cos function) called the interaction between a lump and two-line solitons. At the critical point, the second-order derivative and the Hessian matrix for only one point will be investigated and the lump solution has one maximum value. The moving path of the lump solution and also the moving velocity and the maximum amplitude will be obtained. The graphs for various fractional orders α are plotted to obtain 3D plot, contour plot, density plot, and 2D plot. The physical phenomena of this obtained lump and its interaction soliton solutions are analyzed and presented in figures by selecting the suitable values. That will be extensively used to report many attractive physical phenomena in the fields of fluid dynamics, classical mechanics, physics, and so on.

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Section: Introductionmentioning

confidence: 99%

Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics

et al. 2021

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“…Different types of fractional differential equations of both FODEs and FPDEs in various fields of science like fluid flow, mechanics, biology, and so forth, are expressed in the special forms. [1][2][3][4][5][6][7][8][9][10] There is no any particular method for accessing the exact type solutions of nonlinear PDEs but some approximate and analytical solutions are determine. 11,12 Many nonlinear evolution equations (NLEEs) are presented and studied associated with the soliton and integrable system, which are closely linked with mathematical physics method and variety of mechanical phenomena.…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear fractional partial differential equation is a physical and natural model in which can be constructed by scientists and researchers. Different types of fractional differential equations of both FODEs and FPDEs in various fields of science like fluid flow, mechanics, biology, and so forth, are expressed in the special forms 1‐10 . There is no any particular method for accessing the exact type solutions of nonlinear PDEs but some approximate and analytical solutions are determine 11,12 …”

Section: Introductionmentioning

confidence: 99%

Interaction among a lump, periodic waves, and kink solutions to the fractional generalized CBS‐BK equation

Manafian

Lakestani

2020

Math Methods in App Sciences

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The Hirota bilinear method is prepared for searching the diverse soliton solutions for the fractional generalized Calogero-Bogoyavlenskii-Schiff-Bogoyavlensky-Konopelchenko (CBS-BK) equation. Also, the Hirota bilinear method is used to finding the lump and interaction with two stripe soliton solutions. Interaction among lumps, periodic waves, and multi-kink soliton solutions will be investigated. Also, the solitary wave, periodic wave, and cross-kink wave solutions will be examined for the fractional gCBS-BK equation. The graphs for various fractional order are plotted to contain 3D plot, contour plot, density plot, and 2D plot. We construct the exact lump and interaction among other types solutions, by solving the under-determined nonlinear system of algebraic equations for the associated parameters. Finally, analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed. The existence conditions are employed to discuss the available got solutions.

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“…In numerous distinct branches of science such as mathematics, chemistry, biology, ecology, chaos syncing, mechanics engineering, physics and anomalous spreads, and so on [6][7][8], many researchers have investigated analytical, semiautomatic, and numerical solutions of fractional models. Such phenomena have been modeled by the fractional mathematical models based on experimental results to demonstrate their nonlocal properties, where this form of property [9][10][11][12][13] cannot be expressed by nonlinear partial differential equations with an integer order.…”

Section: Introductionmentioning

confidence: 99%

Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

et al. 2020

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This research uses the extended exp-$( -\varphi(\vartheta ) ) $ ( − φ ( ϑ ) ) -expansion and the Jacobi elliptical function methods to obtain a fashionable explicit format for solutions to the fragmented biological population and the same width models that depict popular logistics because of deaths or births. In mathematical terminology, the linear, hyperbolic, and trigonometric equation solutions that have been found describe several innovative aspects from the two models. Sketching these solutions in different types is used to give them more details. The accuracy and performance of the method adopted show their ability to be applied to various nonlinear developmental equations.

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Solitons and lump wave solutions to the graphene thermophoretic motion system with a variable heat transmission

Cited by 42 publications

References 20 publications

Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics

Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics

Interaction among a lump, periodic waves, and kink solutions to the fractional generalized CBS‐BK equation

Oblique explicit wave solutions of the fractional biological population (BP) and equal width (EW) models

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