Exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr nonlinearity form using two strategic integrations.

Nestor, Savaïssou; Betchewe, Gambo; Doka, Serge Y.

doi:10.1140/epjp/s13360-020-00384-x

Cited by 31 publications

(5 citation statements)

References 22 publications

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“…In equations (5)-( 6), w, κ 1 , L and Θ(z, τ) are respectively the velocity, soliton fRequency, wave number and finally the phase component of the soliton. Note that, the use of equations (5)-( 6) is a technique which aims to transform FPDEs into ODEs by means of the properties of the conformable fractional derivative operator which are subsequently solved to obtain traveling wave solutions to the original model (4). By inserting equations (4)-( 5)- (6) in equation (3), we obtain the following…”

Section: Basic Ideas Of the Two Proposed Methodsmentioning

confidence: 99%

“…Theses features motivates our curiosity to take an interest in a significant and applicable model, namely the perturbed nonlinear Schrödinger equation with conformable space-time fractional form. It is well known that nonlinear Schrödinger equations (NLSEs) are one of important physical models [4,5] which describes a large variety of phenomena, e.g. fluid dynamics, nonlinear optics, condensed matter, acoustics, plasma physics and so on [6,7].…”

Section: Introductionmentioning

confidence: 99%

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A series of abundant new optical solitons to the conformable space-time fractional perturbed nonlinear Schrödinger equation

Nestor¹,

Houwe²,

Betchewe³

et al. 2020

Phys. Scr.

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In this work, we are investigating a series of new optical soliton solutions to the perturbed nonlinear Schrödinger equation (PNLSE) having the form of kerr law nonlinearity with conformable space-time fractional. Thereby, two relevant integration tools known as new extended direct algebraic method and extended hyperbolic function method are applied to obtain varieties of optical soliton solutions. The series of soliton solutions with fractional derivative order obtained by these methods can be classified as complex trigonometric and hyperbolic functions as well as other elementary functions. Furthermore, conditions for validity of the obtained analytical solutions, graphical illustration (2-D, 3-D) point out the impact of the fractional-order used.

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Section: Basic Ideas Of the Two Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A series of abundant new optical solitons to the conformable space-time fractional perturbed nonlinear Schrödinger equation

Nestor¹,

Houwe²,

Betchewe³

et al. 2020

Phys. Scr.

Self Cite

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show abstract

“…Because of its extraordinary physically meaningful properties, the NLSE describes a wide variety of phenomena, such as nonlinear optics [1], Bose-Einstein condensation [2,3], plasma ion acoustic wave [4,5], optical communication [6,7], fluid dynamics [8,9] etc. Perturbed nonlinear Schrödinger equation [10][11][12][13][14][15]: iq aq b q q i q q q q q 0, 1.1…”

Section: Introductionmentioning

confidence: 99%

“…AI-Ghafri et al [10] studied the W shape and various types of soliton solutions with different optical soliton structures of the perturbed nonlinear Schrödinger equation by using the analytic method; Sulaiman et al [11] obtained perturbed nonlinear Schrödinger equation optical solitons and periodic wave solutions by applying the extended sinh Gordon method. Nestor et al [12] derived the exact traveling wave solutions of the perturbed nonlinear Schrödinger equation by using the extended sinh Gordon equation expansion method and the extended Jacobi elliptic function method. Triki et al [13] first derived three new nonlinear chirped W shape soliton solutions of the perturbed nonlinear Schrödinger equation by using the traveling wave method.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of traveling wave solutions of the perturbed nonlinear Schrödinger equation

Cheng

Song

2023

Phys. Scr.

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In this paper, the traveling wave solutions of perturbed nonlinear Schr$\ddot{o}$dinger equation in nanofibers are studied by using the bifurcation theory of dynamic systems. The phase portrait and orbit analysis of perturbed nonlinear Schr$\ddot{o}$dinger equation are given in the form of graph, and the traveling wave solutions corresponding to perturbed nonlinear Schr$\ddot{o}$dinger equation under different conditions are derived and analyzed. Moreover, periodic wave solutions and periodic singular wave solutions are obtained by using Jacobian elliptic function on the basis of predecessors. And it was found that the limit of periodic wave solutions is solitary wave solutions. The limit of periodic singular wave solutions is singular wave solutions. These results provide convenience for scholars to study the physical value of this equation and allow for a deeper understanding of nonlinear phenomena and their physical essence in nanofibers.

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“…Therefore, when small disturbances enforced on the continuous waves (CW) grow exponentially, the MI breaks into the nonlinear system which opposes the nonlinearity to the dispersion. A lot of studies in this topic have been carried out in Nestor et al (2020c), Canabarro et al (2016), Bendahane et al (2017), Li et al (2017); Lei et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Optical soliton and weierstrass elliptic function management to parabolic law nonlinear directional couplers and modulation instability spectra

et al. 2021

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This paper shows out optical soliton solutions of the twin-core couplers with parabolic law nonlinearity with optical metamaterials parameters. It is used the improved new sub-ODE method (SOM) to found dark optical soliton, trigonometric function solutions, bright optical soliton and Jacobian elliptic function (JEF) solutions. Besides, physical explanation of the obtained bright and dark optical soliton solutions have been done and the influence of some parameters of the model have been set out. As the two-core coupler is favorable for modulation instability (MI), it has been studied the steady state of the results. More importantly, we have checked the effects of the optical metamaterials parameters on the formation of the Modulation bands in normal and anomalous dispersive regime. The results obtained in this paper set out Weierstrass Elliptic Function solutions compared to Mirzazadeh et al.

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Exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr nonlinearity form using two strategic integrations.

Cited by 31 publications

References 22 publications

A series of abundant new optical solitons to the conformable space-time fractional perturbed nonlinear Schrödinger equation

A series of abundant new optical solitons to the conformable space-time fractional perturbed nonlinear Schrödinger equation

Bifurcation of traveling wave solutions of the perturbed nonlinear Schrödinger equation

Optical soliton and weierstrass elliptic function management to parabolic law nonlinear directional couplers and modulation instability spectra

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