Nonlinear Schrödinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions

Yıldırım, Yakup; Çelik, Nisa

doi:10.1016/j.rinp.2017.08.008

Cited by 23 publications

(4 citation statements)

References 13 publications

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“…The Kerr law of nonlinearity emerges when a light wave in an optical fiber meets nonlinear responses because of nonharmonic mobility of electrons trapped in molecules produced by an external electric field [ 206 ]. Solli and colleagues observed for the first time the rogue waves in one-dimensional settings in the field of optics [ 207 ].…”

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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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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“…Bhrawy et al added to those results the cases of polynomial and triple-power laws by using the travelling wave hypothesis [2]. Very recently, Yıldırım et al constructed systematically dark, bright and singular soliton solutions of model equation by extended Kudryashov's algorithm [23]. In addition to those papers, Biswas et al obtained the dark, singular and singular periodic solutions employing by trial equation method [24].…”

Section: The Governing Mathematical Equation Of Optical Solitons Is Nmentioning

confidence: 99%

Optical solitons of conformable space-time fractional NLSE with Spatio-temporal dispersion

Yaşar¹,

Yaşar²

2018

ntmsci

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In this work, the dynamics of traveling waves of an improved nonlinear space-time fractional Schrödinger's equation with spatio-temporal dispersion in addition to group-velocity dispersion are studied. This equation models the propagation of solitons through nano optical fibers. The fractional derivative form is considered in the meaning of conformable fractional derivative. The exp(−φ (ξ)) algorithm will be carried out for retrieving the optical soliton solutions containing the form of kink and multi-soliton shapes. In addition, some graphical simulations of solutions are provided for better understanding the physical phenomena.

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“…Numerous integral techniques have been applied in investigating numerous optical soliton solutions for several NLSEs. To do that, the extended direct algebraic scheme [14], the novel extended Kudryashov's scheme [15], the expansion integral scheme [16], the Sine-Gordon expansion scheme [17], the Bäcklund transformations method [18], the bifurcation analysis scheme [19], the computational approach [20], and the unified approach [21] are applied. In general, several mathematical approaches have been developed in this context for deriving various nonlinear wave phenomena [22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Stability and spin solitonic dynamics of the HFSC model: effects of neighboring interactions and crystal field anisotropy parameters

Islam,

Sheikh,

Roshid

et al. 2023

Preprint

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This research investigates spin dynamic solitonic wave solutions in the (2 + 1)-dimensional Heisenberg Ferromagnetic Spin Chains model. The unified and simple equation schemes are used to integrate the model. Through the technique, various properties of wave nature, such as Dark bell envelope soliton, Bright bell envelope soliton, periodic wave envelope, Kink shape envelope soliton, periodic wave envelope soliton, oscillating wave, harmonically oscillating wave, oscillating wave with increasing and decreasing amplitude waves, sudden increasing of amplitude and sudden decrease to a particular amplitude wave oscillations, are achieved from the solutions. The effects of changing neighboring interaction and uniaxial crystal field anisotropy parameters on the obtained soliton and its amplitudes are explored. The changing values of neighboring interaction parameters are exhibited as an increase in wave height with increasing parametric values, but increasing the values of the uniaxial crystal field anisotropy parameter causes a reduction in wave height. In the mean time, we see that the real part of the same solution exhibits periodic oscillation while the effects of the parameters have the same increasing and decreasing effects. Analysis of odulation stability found due to small change as perturbation solution of the model. All shapes are illustrated in 3D and 2D plots.

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Nonlinear Schrödinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions

Cited by 23 publications

References 13 publications

A Framework for Biosensors Assisted by Multiphoton Effects and Machine Learning

A Framework for Biosensors Assisted by Multiphoton Effects and Machine Learning

Optical solitons of conformable space-time fractional NLSE with Spatio-temporal dispersion

Stability and spin solitonic dynamics of the HFSC model: effects of neighboring interactions and crystal field anisotropy parameters

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