New optical solitons of cubic-quartic nonlinear Schrödinger equation

Hosseini, K.; Samadani, F.; Kumar, Dipankar; Faridi, M.

doi:10.1016/j.ijleo.2017.11.124

Cited by 94 publications

(32 citation statements)

References 23 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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“…According to this goal, many researchers have been trying to derive analytical techniques for getting explicit wave solutions [1][2][3][4][5][6][7][8][9][10]. Many kinds of solutions are obtained, such as trigonometric, exponential, hyperbolic, periodic, rational, and elliptic solutions [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Analytical and semi-analytical wave solutions for longitudinal wave equation via modified auxiliary equation method and Adomian decomposition method

et al. 2019

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Original scientific paper https://doi.org/10.2298/TSCI190221355A This paper studies the analytical and semi-analytical wave solutions for the longitudinal wave equation. Moreover, it examines the performance of the modified auxiliary equation method and Adomian decomposition method on this model. This model describes the dispersion in the circular rod that dispersion caused by the transverse Poisson's effect in electro-magneto-elastic. Many explicit wave solutions are found by using the analytical technique. These solutions allow studying the physical properties of this model. The comparison between the analytical and semi-analytical solutions is discussed to show the value of the absolute error between them.

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“…The countless applications of nonlinear evolution equations (NLEEs) in diverse scientific fields have attracted the attention of many academic scholars to search and analyze their exact solutions. In this respect, various methods such as the Kudryashov method [1][2][3][4][5][6][7], tanh-coth method [8,9], modified simple equation method [10,11], sine-cosine method [12,13], transformed rational function method [14,15], ansatz method [16,17], auxiliary equation method [18,19], semi-inverse variational method [20,21], and exp a -function method [22][23][24] have been utilized to solve and handle the NLEEs.…”

Section: Introductionmentioning

confidence: 99%

High-Order Dispersive Cubic-Quintic Schrödinger Equation and Its Exact Solutions

et al. 2019

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The light pulses propagation in optical fibers modeled by the dispersive cubic-quintic Schrödinger equation including high-order time derivatives is investigated in detail. For this purpose, the exp a-function scheme is utilized along with a symbolic computation system to gain the exact solutions of the model. As an outcome, a wide range of exact solutions including dark and periodic solitary wave solutions are effectively derived, verifying the excellent performance of the scheme.

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New optical solitons of cubic-quartic nonlinear Schrödinger equation

Cited by 94 publications

References 23 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 and semi-analytical wave solutions for longitudinal wave equation via modified auxiliary equation method and Adomian decomposition method

High-Order Dispersive Cubic-Quintic Schrödinger Equation and Its Exact Solutions

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