Analytical optical soliton solutions of the Schrödinger-Poisson dynamical system

Younis, Muhammad; Seadawy, Aly R.; Baber, Muhammad Zafarullah; Husain, S.A.; Iqbal, Muhammad Sajid; Rizvi, Syed T. R.; Băleanu, Dumitru

doi:10.1016/j.rinp.2021.104369

Cited by 57 publications

(10 citation statements)

References 38 publications

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“…The obtained solutions show the regular charge distribution for all conducting materials as well as its show significant the quantum state that produces coupling between different gravity states. The novelties of our obtained solutions appear when we compared it's with that realized before by [33] who use (G'/G)-expansion method and the extended direct algebraic methods. Furthermore, the numerical solutions corresponding to the achieved analytical solutions have been constructed by using the two-dimensional differential transform method.…”

Section: Discussionmentioning

confidence: 83%

“…The idea of differential transform was first introduced by Zhou [32], who used it to solve linear and nonlinear initial value problems in electric circuit analysis. Chen and Ho [33] extended this method for partial differential equations PDEs and got on a closed form series solutions for linear and nonlinear initial value problems. The method applied to PDEs, is called two-dimensional differential transform method (TDDTM) [34][35][36], this method is different from the high-order Taylor series method, which consists of computing the coefficients of the Taylor series of the solution using the initial data and the partial differential equation.…”

Section: Numerical Treatment For the Schrödinger-poisson Dynamical Sy...mentioning

confidence: 99%

“…In related subject, we will use the two-dimensional differential transform method [28][29][30][31][32] to obtain the numerical solutions corresponding to the achieved analytical solutions. The Schrödinger -Poisson dynamical system [33] can be written as When this system is surrenders to the definition of  it will be converted to…”

Section: Introductionmentioning

confidence: 99%

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New impressive analytical optical soliton solutions to the Schrödinger–Poisson dynamical system against its numerical solutions

2023

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In our current study, we will derive new diverse enormous impressive analytical optical soliton solutions for the Schrödinger-Poisson dynamical system. The proposed model is applied in gravity field with the corresponding quantum state that produces coupling between different gravity states. Moreover, this model has a significant role in the field of many quantum phenomena. Hereby, we will construct diverse forms of the soliton behaviors that arising from this dynamical system via the solitary wave ansatze method. This technique is one of the ansatze methods that doesn't surrenders to the homogeneous balance and continuously achieves good results. Moreover, we will construct the numerical solutions that are identical for all achieved exact solutions by using two-dimensional differential transform method (TDDTM). The extracted soliton solutions are new compared with that realized before by other authors who used various techniques. The achieved solutions will give new distinct configurations to soliton behaviors arising from this model and show the fact of charges regular distributions on conductors' materials surface.

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Section: Discussionmentioning

confidence: 83%

Section: Numerical Treatment For the Schrödinger-poisson Dynamical Sy...mentioning

confidence: 99%

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New impressive analytical optical soliton solutions to the Schrödinger–Poisson dynamical system against its numerical solutions

2023

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“…The different numerical schemes include the forward Euler difference scheme [13], the non-standard finite difference scheme [14], the backward Euler difference scheme [15], the implicit finite difference scheme [16], the Crank-Nikolson finite difference scheme [17], etc. On the other hand, to find exact solutions many analytical techniques are used to explore exact solutions for nonlinear PDEs, such as the new modified extended direct algebraic method [18], the G ′ /G-model expansion method [19], the Riccati equation mapping method [20], the Hirota bilinear method [21,22], the modified exponential rational function method [23], and the ϕ 6 -model expansion method [24].…”

Section: Introductionmentioning

confidence: 99%

Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing

Baber,

Ahmed,

Yasin

et al. 2024

Mathematics

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This study deals with a stochastic reaction–diffusion biofilm model under quorum sensing. Quorum sensing is a process of communication between cells that permits bacterial communication about cell density and alterations in gene expression. This model produces two results: the bacterial concentration, which over time demonstrates the development and decomposition of the biofilm, and the biofilm bacteria collaboration, which demonstrates the potency of resistance and defense against environmental stimuli. In this study, we investigate numerical solutions and exact solitary wave solutions with the presence of randomness. The finite difference scheme is proposed for the sake of numerical solutions while the generalized Riccati equation mapping method is applied to construct exact solitary wave solutions. The numerical scheme is analyzed by checking consistency and stability. The consistency of the scheme is gained under the mean square sense while the stability condition is gained by the help of the Von Neumann criteria. Exact stochastic solitary wave solutions are constructed in the form of hyperbolic, trigonometric, and rational forms. Some solutions are plots in 3D and 2D form to show dark, bright and solitary wave solutions and the effects of noise as well. Mainly, the numerical results are compared with the exact solitary wave solutions with the help of unique physical problems. The comparison plots are dispatched in three dimensions and line representations as well as by selecting different values of parameters.

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“…In this modern era of research, finding soliton solutions is an important field to describe the physical behavior of the nonlinear PDEs. There are many different techniques to find the soliton solutions such as G /G expansion method https://www.journals.vu.lt/nonlinear-analysis [4,31], first integral method [5], Kudryashov method [3,8], generalized logistic equation method [22,34], Riccati mapping method [2,33], φ 6 -model expansion method [27,35], He's variational method [20], generalized exponential rational function method [12], Hirota bilinear method [11], modified exponential rational functional method [1], a new auxiliary equation [28], Riccati-Bernoulli sub-ODE method [7,16,19], etc. But in this study, we apply the new modified extended direct algebraic method and the existence of the solutions on the bistable Allen-Cahn equation with quartic potential.…”

Section: Introductionmentioning

confidence: 99%

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

Iqbal¹,

İnç

Sohail

et al. 2023

NAMC

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In this paper, the examination of soliton solutions of the biofilm model with the help of a new extended direct algebraic method is expressed. Besides the exact solutions, the existence of these solutions is also discussed with the help of the Schauder fixed point theorem. The nonlinear dynamical biofilm model which we consider in this paper is basically the bistable Allen–Cahn equation with quartic potential. For more physical understanding, the 3D plots of the solutions are presented. The different types of hyperbolic, trigonometric, and rational soliton solutions are gained. In the biofilm model, different parameters belong to certain spaces and give the exact solutions by applying the technique of new extended direct algebraic method. Exact solutions of the biofilm model are highlighted along with their restriction.

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Analytical optical soliton solutions of the Schrödinger-Poisson dynamical system

Cited by 57 publications

References 38 publications

New impressive analytical optical soliton solutions to the Schrödinger–Poisson dynamical system against its numerical solutions

New impressive analytical optical soliton solutions to the Schrödinger–Poisson dynamical system against its numerical solutions

Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing

Analysis and soliton solutions of biofilm model by new extended direct algebraic method

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