Cubic–quartic optical solitons in Kerr and power law media

Biswas, Anjan; Triki, Houria; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Belić, Milivoj R.

doi:10.1016/j.ijleo.2017.07.008

Cited by 148 publications

(41 citation statements)

References 11 publications

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“…The non-linear Schrödinger equation is a generalized (1+1)-dimensional version of the Ginzburg-Landau equation presented in 1950 in their study on supraconductivity and has been specifically reported by Chiao et al [1] in their research of optical beams. In the past several years, various methods have been proposed to obtain the exact optical soliton solutions of the non-linear Schrödinger equation [2][3][4][5][6][7][8][9][10][11][12]. Dispersion and non-linearity are two of the essential components for the distribution of solitons across inter-continental regions.…”

Section: Introductionmentioning

confidence: 99%

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

et al. 2020

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The research paper aims to investigate the space-time fractional cubic-quartic non-linear Schrödinger equation in the appearance of the third, and fourth-order dispersion impacts without both group velocity dispersion, and disturbance with parabolic law media by utilizing the extended sinh-Gordon expansion method. This method is one of the strongest methods to find the exact solutions to the non-linear partial differential equations. In order to confirm the existing solutions, the constraint conditions are used. We successfully construct various exact solitary wave solutions to the governing equation, for example, singular, and dark-bright solutions. Moreover, the 2D, 3D, and contour surfaces of all obtained solutions are also plotted. The finding solutions have justified the efficiency of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

et al. 2020

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“…In the past, solitons in optical metamaterials have been studied with various forms of non-Kerr laws of nonlinearity where several integration schemes have been implemented [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The interested reader also read herein references [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. This paper is going to revisit the study of solitons in optical metamaterials for a specific form of nonlinear medium.…”

Section: Introductionmentioning

confidence: 99%

Analytical treatment in optical metamaterials with anti-cubic law of nonlinearity by IEFM and EShGEEM

İlhan

Manafian

2019

Rev. Mex. Fís.

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Here, the improved exp(−Ω())-expansion method (IEFM) and extended sinh-Gordon equation expansion method (EShGEEM)are being applied on (1+2)-dimensional nonlinear Schr¨odinger equation, optical metamaterials, with anti-cubic nonlinearity. Materialslike photovoltaic-photorefractive, polymer and organic consists of spatial solitons and optical nonlinearities, which can beidentified by seeking help from NLSE with anti-cubic nonlinearity. Abundant exact traveling wave solutions consisting of freeparameters are established in terms of bright, dark, singular, kink-singular, and combined dark-bright soliton solutions. Variousarbitrary constants obtained in the solutions help us to discuss the graphical behavior of solutions and also grants flexibilityto formulate solutions that can be linked with a large variety of physical phenomena. Moreover, graphical representation ofsolutions are shown vigorously in order to visualize the behavior of the solutions acquired for the equation.

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“…In the past, solitons in optical metamaterials have been studied with various forms of non-Kerr laws of nonlinearity where several integration schemes have been implemented [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Interested reader also read herein references [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. This paper is going to revisit the study of solitons in optical metamaterials for a specific form of nonlinear medium.…”

Section: Introductionmentioning

confidence: 99%

Solitons in optical metamaterials with anti-cubic law of nonlinearity by ETEM and IGEM

Foroutan

Manafian

2018

J. Eur. Opt. Soc.-Rapid Publ.

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Background: This paper studies soliton perturbation in optical metamaterials, with anticubic nonlinearity. Methods: Two integration approaches, namely, the extended trial equation method (ETEM) and the improved G'/Gexpansion method (IGEM) are presented. Results: Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons in metamaterials are also demonstrated. All solutions have been verified back into its corresponding equation with the aid of maple package program. Conclusions: Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in optical metamaterials.

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Cubic–quartic optical solitons in Kerr and power law media

Cited by 148 publications

References 11 publications

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

Exact Soliton Solutions to the Cubic-Quartic Non-linear Schrödinger Equation With Conformable Derivative

Analytical treatment in optical metamaterials with anti-cubic law of nonlinearity by IEFM and EShGEEM

Solitons in optical metamaterials with anti-cubic law of nonlinearity by ETEM and IGEM

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