Dark soliton control based on dispersion and nonlinearity for third-order nonlinear Schrödinger equation

Wang, Chenjian; Nie, Zizhuo; Xie, Weijie; Gao, Jingyi; Zhou, Qin; Liu, Wenjun

doi:10.1016/j.ijleo.2019.04.020

Cited by 53 publications

(11 citation statements)

References 47 publications

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“…There are different methods to determine the optical solutions [2][3][4][5][6][7][8][9] of nonlinear partial differential equations but the Lie symmetry technique [10][11][12][13] is a powerful tool. The non-trivial exact solutions of Einstein's field equations are found by using Lie symmetries in [14][15][16] etc.…”

Section: Introductionmentioning

confidence: 99%

On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

et al. 2021

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Section: Introductionmentioning

confidence: 99%

On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

et al. 2021

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“…On the other hand, optical solitons is one of the vital areas of research in the field of nonlinear optics (Adem et al 2020;Javed et al 2020;Al Khawaja and Al-Marzoug 2020;Hari et al 2020;El-Borai et al 2017;Biswas et al 2019;Awan et al 2021;Seadawy et al 2021;Ahmed et al 2020;El-Sheikh et al 2019a, b, 2020Tahir and Awan 2020;Yldrm 2019Yldrm , 2021Liu et al 2016Liu et al , 2017aLiu et al , b, c, 2018Yan et al 2020;Fan et al 2019;Wang et al 2019). Magneto-optic wave guides can help to reduce solitons clutter, to solve the internet bandwidth issue and other such injurious features (Biswas 2004;Tien 1971).…”

Section: Introductionmentioning

confidence: 99%

Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Ahmed

Rabie

2021

Opt Quant Electron

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In this paper, we apply modified extended direct algebraic method to obtain optical soliton solutions in magneto-optic waveguides with dual-power law nonlinearity. Dark, bright, singular, bright-dark combo and singular-bright combo soliton solutions are obtained. Also, periodic solutions and Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, 3D and 2D graphs are presented.

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“…In particular, the third-order dispersion (TOD), Raman scattering (RS) and self-steepening (SS) affects the dynamics of solitons propagating in NLDC [31], [32]. Study the propagation of ultrashort pulses in a coupler is practically important in various areas of research; these are studied in nonlinear optics, plasma physics, nuclear physics, mathematical physics, bio-physics and many other physical sciences [33], [34], [35], [36]. In addition, recently practical applications of these solitons include high-order nonlinearities in couplers are applied in medical devices, such as new researches of Sydney University examine the usage of ultrashort pluses to improve the eye surgery devices [37].…”

Section: Introductionmentioning

confidence: 99%

Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

Safaei

Hatami

Zarandi

2021

Preprint

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In this paper, we analytically solve the coupled equations of a PT -Symmetric NLDC by considering high-order dispersion and nonlinear effects (Raman Scattering and self-steeping) simultaneously in normal dispersion regime. To the best of knowledge no works has been done in previous studies to decoupled these equations and obtain an exact analytical solution. The new exact bright solitary solutions are derived. In addition, to study the stability and instability of these propagated solitons in a PT -Symmetric NLDC, perturbation theory is used. Numerical methods are applied to find perturbed eigenvalues and eigenfunctions. The Stability of obtained four perturbed eigenvalues and perturbed eigenfunctions for a PT -Symmetric NLDC equations regard to high-order effects are examined. Using these results and simulating the propagation of perturbed temporal bright solitons through PT -Symmetric NLDC show that perturbed solitons are mostly stable. This means that high-order dispersion and nonlinear effects canceled each other and do not affected the propagated solitons. Furthermore, the evolution of perturbed solitons energies match well the previous results and con rmed the stability of these solitons in a PT -Symmetric NLDC. As seen the energies of pulses in bar and cross behave in two manner 1) the exchange of energy is happened in some periods, but the shape of each pulse in bar and cross is preserved. Therefore, the solitons under this eigenfunction perturbation are mostly stable. 2) the evolution of energy in the bar and cross, demonstrate that there is no changes in their energies and they remain constant. It is straightforward to show that in spite of considering high-order effects, the perturbed soliton conserve the shape and it remain stable. The deliverables of this article not only demonstrate a novel approach to ultra-fast pulses, solitons and optical couplers, but more fundamentally, they could give insight for improving the new medical equipments technologies, enabling innovations in nonlinear optics and their usage in designing new communication systems and Photonic devices.

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Dark soliton control based on dispersion and nonlinearity for third-order nonlinear Schrödinger equation

Cited by 53 publications

References 47 publications

On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

Structure of optical solitons in magneto–optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method

Stability of Soliton Solutions For A PT- Symmetric NLDC Considering High-Order Dispersion and Nonlinear Effects Simultaneously

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