Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm

Jhangeer, Adil; Faridi, Waqas Ali; Asjad, Muhammad Imran; Akgül, Ali

doi:10.1016/j.padiff.2021.100102

Cited by 28 publications

(13 citation statements)

References 23 publications

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“…The physical significance of these solitons is shown in terms of modulus of uðx, tÞ by assigning particular values of free parameters. Equations ( 23) and (30) show the same graphical behavior with just translation given in Equation (4) as in the figures. In Figures 1 and 2, these solitons in the form of 3D plots for fractal dimension value γ = 0:8 and 2D graphs for γ = 0:5,0:7,0:9 are provided.…”

Section: Resultsmentioning

confidence: 57%

“…This paper introduces the fractal double-chain DNA model to scrutinize the double-helix structure. Fractal calculus has been a flourishing subject of biology, mathematics, and physics because it deals with the modeling of distinct nonlinear procedures [27][28][29][30][31][32][33][34]. Since the fractal model covers many powerful properties, which the traditional system fails to explain.…”

Section: Introductionmentioning

confidence: 99%

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New Fractal Soliton Solutions and Sensitivity Visualization for Double-Chain DNA Model

Hassan

Raza

Abdel‐Aty

et al. 2022

Journal of Function Spaces

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This article discusses dynamics of the fractal double-chain deoxyribonucleic acid model. This structure contains two long elastic homogeneous strands that serve as two polynucleotide chains of deoxyribonucleic acid molecules, bounded by an elastic membrane indicating hydrogen bonds between the base pairs of two chains. The semi-inverse variational principle and auxiliary equation method are employed to extricate soliton solutions. The collection of retrieved exact solutions includes bright, dark, periodic, and other solitons. The constraint conditions emerge naturally which ensure the presence of these solutions. Additionally, 2D and 3D graphs showing the impact of fractals on solutions are included. These plots use appropriate parameter values. Furthermore, sensitivity analysis of the considered model is also acknowledged. The outcomes reveal that these techniques are reliable, effective, and applicable to various biological systems.

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Section: Resultsmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

New Fractal Soliton Solutions and Sensitivity Visualization for Double-Chain DNA Model

Hassan

Raza

Abdel‐Aty

et al. 2022

Journal of Function Spaces

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“…Chalcogenide glass, which has a very strong Kerr effect and reacts right away to electrical stimulation, was employed by Gopalakrishnan and colleagues to obtain experimentally meaningful values for the above described [ 208 ]. Jhangeer and his colleagues developed an algorithm capable of obtaining wave solutions of exact paths of complex nonlinear partial differential equations [ 209 ]. This is achieved by improving the perturbative nonlinear Schrödinger equation with the nonlinear Kerr effect, which is an important equation for soliton testing in optical communication networks.…”

Section: Nlo Processes Analyzed With MLmentioning

confidence: 99%

A Framework for Biosensors Assisted by Multiphoton Effects and Machine Learning

et al. 2022

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The ability to interpret information through automatic sensors is one of the most important pillars of modern technology. In particular, the potential of biosensors has been used to evaluate biological information of living organisms, and to detect danger or predict urgent situations in a battlefield, as in the invasion of SARS-CoV-2 in this era. This work is devoted to describing a panoramic overview of optical biosensors that can be improved by the assistance of nonlinear optics and machine learning methods. Optical biosensors have demonstrated their effectiveness in detecting a diverse range of viruses. Specifically, the SARS-CoV-2 virus has generated disturbance all over the world, and biosensors have emerged as a key for providing an analysis based on physical and chemical phenomena. In this perspective, we highlight how multiphoton interactions can be responsible for an enhancement in sensibility exhibited by biosensors. The nonlinear optical effects open up a series of options to expand the applications of optical biosensors. Nonlinearities together with computer tools are suitable for the identification of complex low-dimensional agents. Machine learning methods can approximate functions to reveal patterns in the detection of dynamic objects in the human body and determine viruses, harmful entities, or strange kinetics in cells.

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“…e dark, singular, combined dark-singular soliton, singular periodic wave, and rational function solutions for the (2 + 1)-dimensional Biswas-Milovic equation for the description of pulse propagation in optical fiber were constructed [57]. Some authors worked on the nonlinear PDEs including the nonlinear directional couplers in nonlinear optics [58]; an improved perturbed Schrödinger equation with Kerr law nonlinearity in nonlinear optics [59]; the fractional analysis of fusion and fission process in plasma physics [60]; traveling, periodic, quasiperiodic, and chaotic structures of perturbed Fokas-Lenells model [61]; and dynamics of longitudinal bud equation among a magnetoelectro-elastic round rod [62]. In Reference [63], the (G'/G)expansion and the Ricatti transformation method were used for solving the (2 + 1)-dimensional Boussinesq equation.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Behaviors of Lumpoff and Rogue Wave Solutions for Nonlocal Gardner Equation

Manafian

Takami

Eslami

et al. 2022

Mathematical Problems in Engineering

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In this paper, we got a novel kind of rogue waves with the predictability of (2 + 1)-dimensional nonlocal Gardner equation with the aid of Maple according to the Hirota bilinear model. We first construct a general quadratic function to derive the general lump solution for the mentioned equation. At the same time, the lumpoff solutions are demonstrated with more free autocephalous parameters, in which the lump solution is localized in all directions in space. Moreover, when the lump solution is cut by twin-solitons, special rogue waves are also introduced. Based on the data available in the literature, the resulting soliton solutions are innovative, developed, distinctive, and significant and can be applied to more complex phenomena, and they are immensely active for nonlinear models of classical and fractional-order type. To examine the dynamic behavior of the waves, contour 3D and 2D plots of several obtained findings are sketched by assigning specific values to the parameters. Furthermore, we obtain new sufficient solutions containing cross-kink, periodic-kink, multi-waves, and solitary wave solutions. It is worth noting that the emerging time and place of the rogue waves depend on the moving path of the lump solution.

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Analytical study of soliton solutions for an improved perturbed Schrödinger equation with Kerr law non-linearity in non-linear optics by an expansion algorithm

Cited by 28 publications

References 23 publications

New Fractal Soliton Solutions and Sensitivity Visualization for Double-Chain DNA Model

New Fractal Soliton Solutions and Sensitivity Visualization for Double-Chain DNA Model

A Framework for Biosensors Assisted by Multiphoton Effects and Machine Learning

Dynamical Behaviors of Lumpoff and Rogue Wave Solutions for Nonlocal Gardner Equation

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