Optical solitons for Lakshmanan–Porsezian–Daniel model by modified simple equation method

Biswas, Anjan; Yıldırım, Yakup; Yaşar, Emrullah; Zhou, Qin; Moshokoa, Seithuti P.; Belić, Milivoj R.

doi:10.1016/j.ijleo.2018.01.100

Cited by 179 publications

(29 citation statements)

References 9 publications

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“…Further, for the future work, the considered non-linear model can be analysed with the help of recently introduced and natured algorithm with great accuracy. [67][68][69] Lastly, we can conclude that the projected method is extremely methodical and more effective, and which can be applied to analyse the diverse classes of complex non-linear problems arising in science and technology.…”

Section: Discussionmentioning

confidence: 95%

“…The present investigation helps the researchers to study the behaviour non‐linear complex problems, particularly the nature of their imaginary part with the aid of contour plots, and this gives very interesting and useful consequences. Further, for the future work, the considered non‐linear model can be analysed with the help of recently introduced and natured algorithm with great accuracy . Lastly, we can conclude that the projected method is extremely methodical and more effective, and which can be applied to analyse the diverse classes of complex non‐linear problems arising in science and technology.…”

Section: Resultsmentioning

confidence: 99%

“…Further, for the future work, the considered non-linear model can be analysed with the help of recently introduced and natured algorithm with great accuracy. [67][68][69] Lastly, we can…”

Section: Discussionmentioning

confidence: 99%

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An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

et al. 2020

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In this paper, the q‐homotopy analysis transform method (q‐HATM) is applied to find the solution for the fractional Lakshmanan‐Porsezian‐Daniel (LPD) model. The LPD model is the generalization of the non‐linear Schrödinger (NLS) equation. The proposed method is graceful fusions of Laplace transform technique with q‐homotopy analysis scheme, and the derivative is considered in Caputo sense. In order to validate and illustrate the efficiency of the proposed method, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured for the three different cases in terms of 3D and contour plots for diverse values of the fractional order. The obtained results confirm that the future method is easy to implement, highly methodical, and very effective to analyse the behaviour of complex non‐linear fractional differential equations exist in the connected areas of science and engineering.

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Section: Discussionmentioning

confidence: 95%

Section: Resultsmentioning

confidence: 99%

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An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

et al. 2020

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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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“…The extended trial function method has been utilized on LPD model includes Kerr and power laws to retrieve bright solitons, dark solitons and periodic solitary waves [12]. The singular and dark soliton solutions to the model have been constructed by using the modified simple equation method [16]. In Ref.…”

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confidence: 99%

Abundant novel solutions of the conformable Lakshmanan-Porsezian-Daniel model

Ismael¹,

Baskonus²

2021

DCDS-S

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In this paper, three images of nonlinearity to the fractional Lakshmanan Porsezian Daniel model in birefringent fibers are investigated. The new bright, periodic wave and singular optical soliton solutions are constructed via the m + G G expansion method, which are applicable to the dynamics within the optical fibers. All solutions are novel compared with solutions obtained via different methods. All solutions verify the conformable Lakshmanan-Porsezian-Daniel model and also, for the existence the constraint conditions are utilized. Moreover, 2D and 3D for all solutions are plotted to more understand its physical characteristics.

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Optical solitons for Lakshmanan–Porsezian–Daniel model by modified simple equation method

Cited by 179 publications

References 9 publications

An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

An efficient analytical approach for fractional Lakshmanan‐Porsezian‐Daniel model

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

Abundant novel solutions of the conformable Lakshmanan-Porsezian-Daniel model

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