Explicit wave phenomena to the couple type fractional order nonlinear evolution equations

Khatun, M. Ayesha; Arefin, Mohammad Asif; Uddin, M. Hafiz; Băleanu, Dumitru; Akbar, M. Ali

doi:10.1016/j.rinp.2021.104597

Cited by 22 publications

(4 citation statements)

References 31 publications

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“…In engineering wave problems, the exact solution of the high-dimensional model of wave propagation has more significant applications [24][25][26][27]. For the solution of nonlinear equations, after the efforts of relevant scholars in recent decades, many accurate methods have been developed, such as inverse scattering method [28], hyperbolic tangent method [29], extended hyperbolic function method [30][31][32], Jacobi elliptic function expansion method and its extended form [33][34][35], F-function expansion method [36], exponential function method [37], Kudryashov method [38], Riccati function expansion method [39], Khater method [40], sine-cosine method [41], (G /G) function expansion method [42,43], (G /G,1/G) function expansion method [44], (1/G) function expansion method [45], (1/G') function expansion method [46], (G /G2) function expansion method [47], extended (G /G) function expansion method [48,49]. Among these methods, the extended (G /G) expansion method [48] is relatively simple, but the author of this method has not carefully studied the mechanism of the extended (G /G) expansion method to obtain new forms of exact solutions compared with the (G /G) expansion method.…”

Section: Introductionmentioning

confidence: 99%

Evolution Analysis of Strain Waves for the Fractal Nonlinear Propagation Equation of Longitudinal Waves in a Rod

Fan,

Liu,

Wang

et al. 2023

Fractal Fract

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Based on the layered and porous characteristics of functionally graded materials and the finite deformation assumption of solids, the fractal nonlinear propagation equation of longitudinal waves in a functionally graded rod is derived. A large number of exact displacement gradient traveling wave solutions of the fractal equation are obtained by using an equivalent simplified extended (G′/G) expansion method. Three sets of existing and different displacement gradient solutions are obtained by analyzing these exact solutions, and then three corresponding fractal dimension strain waves are derived. The results of numerical simulation of the evolution of these three strain waves with fractal dimension show that when the strain wave propagates in the rod, the smaller the fractal dimension or, the larger the radius of the rod, the higher the tensile strength of the material.

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Section: Introductionmentioning

confidence: 99%

Evolution Analysis of Strain Waves for the Fractal Nonlinear Propagation Equation of Longitudinal Waves in a Rod

Fan,

Liu,

Wang

et al. 2023

Fractal Fract

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“…These equations are crucial tools for comprehending the physical analogies and variations in the nonlinear behaviour of dispersive waves. Rogue waves in nonlinear dispersive media are very thought provoking, for example, [16][17][18][19][20] . These rogue waves were initially examined in the background of water waves, and after that, they became an interesting topic for in-depth studies of nonlinear optics.…”

Section: Introductionmentioning

confidence: 99%

Construction of Novel Bright-Dark Solitons and Breather Waves of Unstable Nonlinear Schrödinger Equations with Applications

et al. 2022

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The unstable nonlinear Schrödinger equations (UNLSEs) are universal equations of the class of nonlinear integrable systems, which reveal the temporal changing of disruption in slightly stable and unstable media. In current paper, an improved auxiliary equation technique is proposed to obtain the wave results of UNLSE and modified UNLSE. Numerous varieties of results are generated in the mode of some special Jacobi elliptic functions and trigonometric and hyperbolic functions, many of which are distinctive and have significant applications such as pulse propagation in optical fibers. The exact soliton solutions also give information on the soliton interaction in unstable media. Furthermore, with the assistance of the suitable parameter values, various kinds of structures such as bright-dark, multi-wave structures, breather and kink-type solitons, and several periodic solitary waves are depicted that aid in the understanding of the physical interpretation of unstable nonlinear models. The various constructed solutions demonstrate the effectiveness of the suggested approach, which proves that the current technique may be applied to other nonlinear physical problems encountered in mathematical physics.

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“…e exact traveling wave solutions of fractional partial differential equations have attracted much attention from mathematicians and engineering experts [1][2][3][4][5][6][7][8][9][10]. In recent years, some methods for constructing fractional partial differential equations have been proposed, such as the fractional double function method [11], improved fractional subequation method [12], (G ′ /G1/G)-expansion method [13], plane dynamic system analysis method [14], and complete discrimination method of polynomial [15].…”

Section: Introductionmentioning

confidence: 99%

New Classifications of All Single Traveling Wave Solutions of the Fractional Approximate Long Water Wave Equations by Using the Complete Discrimination System

2022

Mathematical Problems in Engineering

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First, our work is to transform the space-time fractional approximate long water wave equations into nonlinear ordinary differential equations via the traveling wave transformation in the sense of conformable fractional derivative. Second, we simplify the nonlinear ordinary differential equations into an ordinary differential equation with only one variable by integration and some transformations. Finally, we can further get all single traveling wave solutions of the space-time fractional approximate long water wave equations by the complete discrimination system for the four-order polynomial method; these solutions include the hyperbolic function solutions, rational function solutions, and implicit solutions.

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Explicit wave phenomena to the couple type fractional order nonlinear evolution equations

Cited by 22 publications

References 31 publications

Evolution Analysis of Strain Waves for the Fractal Nonlinear Propagation Equation of Longitudinal Waves in a Rod

Evolution Analysis of Strain Waves for the Fractal Nonlinear Propagation Equation of Longitudinal Waves in a Rod

Construction of Novel Bright-Dark Solitons and Breather Waves of Unstable Nonlinear Schrödinger Equations with Applications

New Classifications of All Single Traveling Wave Solutions of the Fractional Approximate Long Water Wave Equations by Using the Complete Discrimination System

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