Solitary wave solutions of the cubic-quintic-septic nonlinear Schrödinger equation in fiber Bragg gratings

Kerbouche, M.; Hamaizi, Y.; El-Akrmi, A.; Triki, Houria

doi:10.1016/j.ijleo.2016.07.038

Cited by 8 publications

(6 citation statements)

References 21 publications

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“…with Equation ( 10), the new perturbation expansion for the variable u near the critical wave number c k is needed. A similar problem has been discussed in the literature for waves propagating in different media [8,9].…”

Section: Introductionmentioning

confidence: 78%

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Quintic-Septic Nonlinear Schrödinger Equation with a Third-Order Dispersion Term

Hacinliyan

2022

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

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In the present study, the quintic-septic nonlinear modulation of a longitudinal wave propagating to contribute the dispersive and higher-order nonlinear effects in a generalized cubically nonlinear elastic medium is considered. In recent work, for the modulation of a longitudinal wave, a cubic nonlinear Schrödinger equation with a third-order dispersive term is obtained by using a multi-scale expansion of quasi-monochromatic wave solutions. The thirdquintic-septic longitudinal wave, by choosing specific values of material constants and wave number for which some coefficients of nonlinear terms are disappeared. In this case, a new perturbation expansion is needed to balance nonlinear effects with dispersive effects. As a result, a quintic-septic nonlinear Schrödinger equation with a third-order dispersion term is obtained as a new model that balances quintic-septic nonlinearity with a third-order dispersion term.

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Section: Introductionmentioning

confidence: 78%

“…was obtained as the model for the propagation of femtosecond optical pulses through fiber Bragg grating structure. Solitary wave solutions and dipole solution solutions were also presented in [9] and in [13], respectively.…”

Section: Introductionmentioning

confidence: 99%

Quintic-Septic Nonlinear Schrödinger Equation with a Third-Order Dispersion Term

Hacinliyan

2022

Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi

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“…Such a di®erence between bounded and unbounded nonlinearities can help to understand what nonlinear laws are closer to real experiments. It is known that both unbounded [2][3][4]9,[19][20][21][22][23][24]34 and bounded [55][56][57] theoretical models are used to describe medium's electromagnetic response (the saturation e®ect was found experimentally, see, for example, Ref. 58).…”

Section: Calculations and Discussionmentioning

confidence: 99%

“…nonlinearities are actively studied experimentally [12][13][14][15][16][17][18] as well as theoretically. 2,4,9,10,[19][20][21][22][23][24][25][26] Recent advances in this¯eld allow one to study transverse-electric (TE) wave propagation in a layer¯lled with nonlinear dielectric having permittivity characterized by a polynomial nonlinearity, see Ref. 27.…”

Section: Statement Of the Problem And Introductory Remarksmentioning

confidence: 99%

Electromagnetic wave propagation in a layer with power nonlinearity

Kurseeva

Tikhov

Валовик

2019

J. Nonlinear Optic. Phys. Mat.

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The paper focuses on a problem that describes propagation of transverse-electric (TE) waves in a plane dielectric waveguide filled with nonlinear medium. The nonlinearity is characterized by the power term [Formula: see text], where [Formula: see text], [Formula: see text] are constants and [Formula: see text] is the electric term of the guided electromagnetic field. The layer is located between two half-spaces filled with linear media having constant permittivities. It is proved that the nonlinear problem has infinitely many propagation constants (PCs), whereas the corresponding linear problem has only a finite number of them. The nonlinearity leads to the occurrence of infinitely many nonperturbative solutions of the nonlinear problem. Results of the paper show that the power nonlinearity (for any [Formula: see text]) and Kerr nonlinearity (for [Formula: see text]) produce qualitatively similar outcomes. In addition, the found results allow one to study very important cases of quintic, septimal, etc. nonlinear permittivities in the focusing regime.

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“…This dependence leads to various particular nonlinear laws for the permittivity: cubic (Kerr), quintic, cubic-quintic, polynomial nonlinearities, power nonlinearity with noninteger degree, saturated nonlinearities, and so on. These nonlinearities were actively experimentally [4,5,[38][39][40][41][42][43][44][45][46] as well as theoretically [2,6,9,13,21,32,[35][36][37][47][48][49][50][51][52][53][54][55][56] studied.…”

Section: Statement Of the Problemmentioning

confidence: 99%

How Kerr nonlinearity influences polarized electromagnetic wave propagation

Валовик

2017

URSI Radio Sci. Bull.

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The propagation of electromagnetic TE waves along boundaries of a plane dielectric layer fi lled with a Kerr medium is studied for all possible cases of the problem's parameters. The layer is located between two half-spaces with constant permittivities. The problem is reduced to a nonlinear transmission eigenvalue problem for Maxwell's equations, in which each eigenvalue is a propagation constant of a guided wave. The exact dispersion equation with respect to the eigenvalues (propagation constants) is derived and studied. It is proven that in the presence of the Kerr eff ect, several novel wave-guiding regimes arise, including regimes that have no counterparts in the linear theory. An infi nite number of eigenvalues arise in the focusing case, even if the corresponding linear problem has no solutions (the linear problem always has no more than a fi nite number of solutions). In the defocusing case, only those solutions arise that tend to linear solutions when the nonlinearity coeffi cient vanishes. It is also proven that in the nonlinear case, an infi nite number of eigenvalues do not reduce to the solutions of the corresponding linear problem, even if the nonlinearity coeffi cient tends to zero. Numerical illustrations for the results obtained are provided.

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Solitary wave solutions of the cubic-quintic-septic nonlinear Schrödinger equation in fiber Bragg gratings

Cited by 8 publications

References 21 publications

Quintic-Septic Nonlinear Schrödinger Equation with a Third-Order Dispersion Term

Quintic-Septic Nonlinear Schrödinger Equation with a Third-Order Dispersion Term

Electromagnetic wave propagation in a layer with power nonlinearity

How Kerr nonlinearity influences polarized electromagnetic wave propagation

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