The dynamical behavior for a famous class of evolution equations with double exponential nonlinearities

Alharthi, Mohammed Shaaf; Băleanu, Dumitru; Ali, Khalid K.; Nuruddeen, Rahmatullah Ibrahim; Muhammad, Lawal; Aljohani, Abdulrahman F.; Osman, M. S.

doi:10.1016/j.joes.2022.05.033

Cited by 13 publications

(4 citation statements)

References 45 publications

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“…More comparatively, the present study generalizes many studies, including the integer-order derivative versions of the models considered in [4,6,7]. Moreover, the employed numerical scheme which doubly serves as a semi-analytical method competes with so many methods in the literature, including [28][29][30][31][32][33][34][35][36][37]; while some known robust integration schemes that happen to contend with the two analytical methods of interest in tackling different class of evolution equations include [38][39][40][41][42][43].…”

Section: Discussion Of Resultsmentioning

confidence: 74%

Wave solutions and numerical validation for the coupled reaction-advection-diffusion dynamical model in a porous medium

Mubaraki

Kim²,

Nuruddeen³

et al. 2022

Commun. Theor. Phys.

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The current study examines the special class of a generalized reaction-advection-diffusion dynamical model that is called the system of coupled Burger’s equations. This system plays a vital role in the essential areas of physics, including fluid dynamics and acoustics. Moreover, two promising analytical integration schemes are employed for the study; in addition to the deployment of an efficient variant of the eminent Adomian decomposition method. Three sets of analytical wave solutions are revealed, including exponential, periodic, and dark-singular wave solutions; while an amazed rapidly convergent approximate solution is acquired on the other hand. At the end, certain graphical illustrations and tables are provided to support the reported analytical and numerical results. No doubt, the present study is set to bridge the existing gap between the analytical and numerical approaches with regard to the solution validity of various models of mathematical physics.

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Section: Discussion Of Resultsmentioning

confidence: 74%

Wave solutions and numerical validation for the coupled reaction-advection-diffusion dynamical model in a porous medium

Mubaraki

Kim²,

Nuruddeen³

et al. 2022

Commun. Theor. Phys.

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“…The quest for analytical solutions to nonlinear partial differential equations is essential in scientific and engineering applications since it provides a wealth of information on the mechanisms of complicated physical phenomena. Numerous effective methods have been devised to seek exact solutions for NPDEs in mathematical physics, such as the Burgan et al method [2], the similarity transformations [3], the parabolic equation method [4], the new modified unified auxiliary equation method [5], the G 1 ( ) ¢expansion method [6,7], Jacobi elliptic function expansion (JEFE) method [8], the simplified Hirotaʼs method [9], the Kudrayshov approach and its modified version [10,11], the modified auxiliary expansion method [12], and the generalized exponential rational function method and its modified version [13,14], as well as some numerical methods [15][16][17][18]. Each of these methods has its characteristics, and the simplified Hirota method is commonly used owing to its efficiency and directness.…”

Section: Introductionmentioning

confidence: 99%

Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation

Ali

Yusuf²,

2023

Commun. Theor. Phys.

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In this paper, we analyze the extended Bogoyavlenskii-Kadomtsev-Petviashvili (eBKP) equation utilizing the condensed Hirota's approach. In accordance with a logarithmic derivative transform, we produce solutions for single, double, and triple M-lump waves. Additionally, we investigate the interaction solutions of a single M-lump with a single soliton, a single M-lump with a double soliton, and a double M-lump with a single soliton. Furthermore, we create sophisticated single, double, and triple complex soliton wave solutions. The extended Bogoyavlenskii-Kadomtsev-Petviashvili equation describes nonlinear wave phenomena in fluid mechanics, plasma, and shallow water theory. By selecting appropriate values for the related free parameters, we also create three-dimensional surfaces and associated counter plots to simulate the dynamical characteristics of the solutions offered.

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“…Analytically wise, a number of appealing approaches analytical exist in the open literature for solving diverse evolution equations and nonlinear Schr ö dinger equations. More so, let us recall some of the following wellknown approaches, including, the generalized Riccati equation approach [7][8][9], the modified tanh expansion approach [10][11][12], some integral-based methods approaches [11][12][13][14], the trial equation approach [15,16], the rational ( ) G G ¢ -expansion method [17,18], the Kudryashov analytical approach [19][20][21], the Lie's symmetry approach [22,23], the F-expansion approach [24], the Jacobi elliptic function technique, that is alternatively called the modified auxiliary equation technique [25][26][27][28], the extended exponential rational approach [29], the semi-inverse variational technique [30][31][32], and the first integral and functional variable approaches [33] to state a few; one would equally read [34][35][36][37] and the references therewith for more analytical approaches in this regard. On the other hand, a number of computational approaches are also visible for solving different evolution equations.…”

Section: Introductionmentioning

confidence: 99%

Revisiting (2+1)-dimensional Burgers’ dynamical equations: analytical approach and Reynolds number examination

et al. 2023

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Classical Burgers’ equation is an indispensable dynamical evolution equation that is autonomously devised by Burgers and Harry Bateman in 1915 and 1948, respectively. This important model is featured through a nonlinear partial diﬀerential equation (NPDE). Furthermore, the model plays a crucial role in many areas of mathematical physics, including, for instance, ﬂuid dynamics, traﬃc ﬂow, nonlinear acoustics, turbulence phenomena, and linking convection and diﬀusion processes to state a few. Thus, in the present study, an eﬃcient analytical approach by the name “generalized Riccati equation approach” is adopted to securitize the class of (2 + 1)-dimensional Burgers’ equations by revealing yet another set of analytical structures to the governing single and vector-coupled Burgers’ equations. In fact, the besieged method of the solution has been proven to divulge various sets of hyperbolic, periodic, and other forms of exact solutions. Moreover, the method ﬁrst begins by transforming the targeted NPDE to a nonlinear ordinary diﬀerential equation (NODE), and subsequently to a set of an algebraic system of equations; where the algebraic system is then solved simultaneously to obtain the solution possibilities. Lastly, certain graphical illustrations in 2- and 3-dimensional plots are set to be depicted - featuring the evolutional nature of the resulting structures, and thereafter, analyze the inﬂuence of the Reynolds number Ra on the respective wave proﬁles.

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The dynamical behavior for a famous class of evolution equations with double exponential nonlinearities

Cited by 13 publications

References 45 publications

Wave solutions and numerical validation for the coupled reaction-advection-diffusion dynamical model in a porous medium

Wave solutions and numerical validation for the coupled reaction-advection-diffusion dynamical model in a porous medium

Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation

Revisiting (2+1)-dimensional Burgers’ dynamical equations: analytical approach and Reynolds number examination

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