Protracted study on a real physical phenomenon generated by media inhomogeneities

Almusawa, Hassan; Ali, Khalid K.; Wazwaz, Abdul‐Majid; Mehanna, M.S.; Băleanu, Dumitru; Osman, M. S.

doi:10.1016/j.rinp.2021.104933

Cited by 32 publications

(5 citation statements)

References 25 publications

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“…Many other works have derived solutions from mathematical models with physical relevance. For example, abundant solutions to the (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation were derived in [40]; some solutions have been provided for the electroosmotic force on micropolar pulsatile bloodstream through aneurysm and stenosis of carotid [41]; optical soliton solutions of perturbing time-fractional nonlinear Schrödinger equations [42]; the entropy generation and curvature effect on peristaltic thrusting of (Cu-Al 2 O 3 ) hybrid nanofluid in resilient channel; and N1-soliton solutions for Schrödinger's equation with competing weakly nonlocal and parabolic law nonlinearities [43]. In the present study, that task is still a task to be accomplished, though its achievement will evidently be the topic of some future work.…”

Section: Discussionmentioning

confidence: 99%

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Molina-Holguín,

Urenda-Cázares,

Macías-Díaz

et al. 2024

Fractal Fract

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In this article, a generalized form of the Davey–Stewartson system, consisting of three nonlinear coupled partial differential equations, will be studied. The system considers the presence of fractional spatial partial derivatives of the Riesz type, and extensions of the classical mass, energy, and momentum operators will be proposed in the fractional-case scenario. In this work, we will prove rigorously that these functionals are conserved throughout time using some functional properties of the Riesz fractional operators. This study is intended to serve as a stepping stone for further exploration of the generalized Davey–Stewartson system and its wide-ranging applications.

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Section: Discussionmentioning

confidence: 99%

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Molina-Holguín,

Urenda-Cázares,

Macías-Díaz

et al. 2024

Fractal Fract

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“…After employing Eq (15) with Eq (16) into Eq (6), set of algebraic equations turns up as follows and setting all the factors of the distinct powers of k g equal to zero, we have…”

Section: Plos Onementioning

confidence: 99%

“…Quantum physics that regulates microscopic systems is a best example of the q deformed Sinh-Gordon equation [13]. Numerous partial differential equations in classical calculus that have important applications in numerous fields have been studied by a number of scholars [14][15][16]. These models play an instrumental role both in applied sciences and Mathematics.…”

Section: Introductionmentioning

confidence: 99%

Computation of soliton structure and analysis of chaotic behaviour in quantum deformed Sinh-Gordon model

Jhangeer,

Ibraheem,

Jamal

et al. 2024

PLoS ONE

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Soliton dynamics and nonlinear phenomena in quantum deformation has been investigated through conformal time differential generalized form of q deformed Sinh-Gordon equation. The underlying equation has recently undergone substantial amount of research. In Phase 1, we employed modified auxiliary and new direct extended algebraic methods. Trigonometric, hyperbolic, exponential and rational solutions are successfully extracted using these techniques, coupled with the best possible constraint requirements implemented on parameters to ensure the existence of solutions. The findings, then, are represented by 2D, 3D and contour plots to highlight the various solitons’ propagation patterns such as kink-bright, bright, dark, bright-dark, kink, and kink-peakon solitons and solitary wave solutions. It is worth emphasizing that kink dark, dark peakon, dark and dark bright solitons have not been found earlier in literature. In phase 2, the underlying model is examined under various chaos detecting tools for example lyapunov exponents, multistability and time series analysis and bifurcation diagram. Chaotic behavior is investigated using various initial condition and novel results are obtained.

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“…This work is arranged as, in Section 1, we analyze briefly about the fundamental techniques. The ðG ′ /GÞ-expansion method [25][26][27], the general form of Kudryashov method [28,29], and the extended tanh method [30][31][32][33][34], the analysis of solutions is given in Section 3, in Section 4, we present some illustrative graphs, and a definitive conclusion is presented in Section 5.…”

Section: Introductionmentioning

confidence: 99%

Analytical Soliton Solutions of the Coupled Radhakrishnan‐Kundu‐Lakshmanan Equation via Three Techniques

Ali

Mehanna²,

Matkan

et al. 2022

Journal of Mathematics

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The analytical soliton solutions to the coupled Radhakrishnan-Kundu-Lakshmanan (RKL) model are greatly important for birefringent fibers without the effect of four-wave mixing (4WM). A significant number of general and standard analytical soliton solutions to this model have been extracted using three powerful techniques, namely the generalized Kudryashov’s method, the extended tanh method, and the G ′ / G -expansion method in this article. The schematic profiles of the solitons are sketched using the symbolic mathematical program Mathematica and are presented in two and three dimensions. The reported solutions might be helpful in explaining the RKL equation’s physical significance as well as some other related nonlinear phenomena that appear in engineering and nonlinear sciences.

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Protracted study on a real physical phenomenon generated by media inhomogeneities

Cited by 32 publications

References 25 publications

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Theoretical Investigation on the Conservation Principles of an Extended Davey–Stewartson System with Riesz Space Fractional Derivatives of Different Orders

Computation of soliton structure and analysis of chaotic behaviour in quantum deformed Sinh-Gordon model

Analytical Soliton Solutions of the Coupled Radhakrishnan‐Kundu‐Lakshmanan Equation via Three Techniques

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