Applications of extended modified auxiliary equation mapping method for high-order dispersive extended nonlinear Schrödinger equation in nonlinear optics

Seadawy, Aly R.; Cheemaa, Nadia

doi:10.1142/s0217984919502038

Cited by 127 publications

(16 citation statements)

References 37 publications

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“…Many scientists used distinct schemes to obtain quantum solutions for NLSEs. Chen et al obtained bell shaped, periodic waves, kink shaped, anti kink, Jacobi elliptic solutions and other solitary wave solutions using bifurcation theory for TFRNLSE with parabolic law nonlinearity (Seadawy and Cheemaa 2019a ). Triki et al obtained used so many nonlinearities to get drk and bright solitons with the aid of ansatz method for time dependent RNLSE (Zhang et al.…”

Section: Resultsmentioning

confidence: 99%

“… 2020 ) and Seadawy techniques (Rizvi et al. 2020a , b ; Sarwar and Rashidi 2016 ; Seadawy and Cheemaa 2019a , b ). Here we consider TFRNLSE under parabolic law with weak nonlocal nonlinearity to obtain multiple lump and rogue wave solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Here we consider TFRNLSE under parabolic law with weak nonlocal nonlinearity to obtain multiple lump and rogue wave solutions. The governing model for TFRNLSE is given by Seadawy and Cheemaa ( 2019a ) where is conformable derivative operator in t -direction and . Eq.…”

Section: Introductionmentioning

confidence: 99%

“…Conformal Derivative: then conformable fractional derivative (CFD) of h order is defined as Seadawy and Cheemaa ( 2019a ), …”

Section: Introductionmentioning

confidence: 99%

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Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

et al. 2022

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This article retrieve lump, lump with one kink and rogue wave soliton for the time fractional resonant nonlinear Schrödinger equation with parabolic law having weak nonlocal nonlinearity. According to theory of dynamical systems, Schrödinger equation may be converted into plane systems. We use Hirota bilinear method to obtained these solutions. At the end, we present graphical representation of our results in various dimensions.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Conformal Derivative: then conformable fractional derivative (CFD) of h order is defined as Seadawy and Cheemaa ( 2019a ), …”

Section: Introductionmentioning

confidence: 99%

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Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

et al. 2022

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“…In the paraxial approximation, we can pick

normalℰ ((), x, z, t) true) = u ((), x, z) e^{- ((), italickz - italiciωt)}

, where

u ((), x, z)

is the optical field envelope,

k

is the wave number and

ω

is the carrier frequency. In the paraxial approximation, 28–32 the envelope

u ((), x, z)

of the optical field propagating in the transparent medium with Kerr nonlinearity, obeys the following nonlinear Helmholtz equation in (1 + 1) dimensions 27 :

\frac{\partial^{2} u}{\partial x^{2}} + 2 italicik \frac{\partial u}{\partial z} + \frac{2 k^{2}}{n_{0}} ([], n_{K} {|u|}^{2} + normalΔ n ((), T)) u = 0,

where

n_{K}

denotes the Kerr nonlinearity coefficient and

n_{0}

is the unperturbed refractive index (defined as

n_{0} = italickc / ω

, with

c

the speed of light). Replacing

normalΔ T ((), x)

given by Equation () in the refractive index correction Equation (), and substituting the latter quantity in the (1 + 1) dimensional Helmholtz Equation (), we obtain:

\frac{\partial^{2} u}{\partial x^{2}} + 2 italicik \frac{\partial u}{\partial z} + 2 g ([], {|u|}^{2} - V ((), x)) u = 0,

where we defined:

…”

Section: Propagation Equation and Exact One‐soliton Solutionmentioning

confidence: 99%

Thermal lensing‐induced soliton molecules in β‐phase gallium oxide

Dikandé

Aban

Sunda-Meya

2021

Micro & Optical Tech Letters

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In recent years, beta gallium oxide (β‐Ga2O3) has become the most investigated isomorph of gallium oxide polymorphs, due to the great potential it represents for applications in optoelectronics and photonics for solar technology, particularly in blind ultraviolet photodetector solar cells (SBUV) designs. To optimize its use in these applications, and to identify possible new features, knowledge of its fundamental properties is relevant. In this respect, optical, thermal and electronic properties of β‐Ga2O3 have been studied experimentally, providing evidence of a wide‐band inorganic and transparent semiconductor with a Kerr nonlinearity. Thermo‐optical properties of the material, probed in SBUV sensing experiments, have highlighted a sizable heat diffusion characterized by a temperature gradient along the path of optical beams, quadratic in beam position and promoting a refractive‐index change with temperature. The experimentally observed Kerr nonlinearity together with the thermally induced birefringence, point unambiguously to a possible formation of soliton molecules during propagation of high‐intensity fields in β‐Ga2O3. To put this conjecture on a firm ground we propose a theoretical analysis, based on the cubic nonlinear Schrödinger equation in 1 + 1 spatial dimension, in which thermal lensing creates an effective potential quadratic in the coordinate of beam position. Using the non‐isospectral inverse‐scattering transform method, the exact one‐soliton solution to the propagation equation is obtained. This solution features a bound state of entangled pulses forming a bright‐soliton molecule, in which pulses are more or less entangled depending on characteristic parameters of the system.

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Numerical simulation for a one‐pressure model of two‐phase flows using a new finite volume scheme

Mohamed

Benkhaldoun

Seadawy

2022

Math Methods in App Sciences

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We propose and develop a new finite volume method for a one‐pressure model of two‐phase flows in one and two dimensional, where the first phase is vapor, which is compressible, and the second phase referred to as the liquid phase. This model has complex characteristic values, which poses a numerical difficulty. This scheme consists of a predictor stage and corrector stage. Numerical results are presented for two‐phase flows model in one and two dimensions. It is found that the proposed finite volume scheme offers a robust and accurate approach for solving this model, and this scheme reveals to be robust and efficient for non‐hyperbolic and non‐conservative systems and our scheme does not need complicated Jacobian fields decomposition.

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Applications of extended modified auxiliary equation mapping method for high-order dispersive extended nonlinear Schrödinger equation in nonlinear optics

Cited by 127 publications

References 37 publications

Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity

Thermal lensing‐induced soliton molecules in β‐phase gallium oxide

Numerical simulation for a one‐pressure model of two‐phase flows using a new finite volume scheme

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