Optical solitons and group invariant solutions to Lakshmanan–Porsezian–Daniel model in optical fibers and PCF

Bansal, Anupma; Biswas, Anjan; Triki, Houria; Zhou, Qin; Moshokoa, Seithuti P.; Belić, Milivoj R.

doi:10.1016/j.ijleo.2018.01.114

Cited by 38 publications

(7 citation statements)

References 9 publications

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“…The Lie symmetry analysis is one of the most powerful mathematical tools to handle a nonlinear differential equation from its integrability standpoint [1,2,11]. This methodology has been successfully implemented in several models [12][13][14]. In this section, we try to construct symmetries, symmetry reductions and group invariant solutions to the BE in the presence of surface tension (1) via the classical Lie method [11][12][13].…”

Section: Lie Symmetry Analysismentioning

confidence: 99%

“…This methodology has been successfully implemented in several models [12][13][14]. In this section, we try to construct symmetries, symmetry reductions and group invariant solutions to the BE in the presence of surface tension (1) via the classical Lie method [11][12][13]. For this, let us consider the Lie group of point transformations as…”

Section: Lie Symmetry Analysismentioning

confidence: 99%

See 1 more Smart Citation

Solitary waves, shock waves and conservation laws with the surface tension effect in the Boussinesq equation

Biswas¹,

Vega-Guzman²,

Bansal³

et al. 2023

PEAS

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This paper secures solitary waves, shock waves and singular solitary waves for the Boussinesq equation, which is studied with the inclusion of surface tension. The method of undetermined coefficients has yielded such waves. The Lie symmetry analysis has introduced a fresh perspective to the model. Conserved densities and corresponding conserved quantities are computed using the multiplier approach.

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Section: Lie Symmetry Analysismentioning

confidence: 99%

Section: Lie Symmetry Analysismentioning

confidence: 99%

Solitary waves, shock waves and conservation laws with the surface tension effect in the Boussinesq equation

Biswas¹,

Vega-Guzman²,

Bansal³

et al. 2023

PEAS

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“…In the context of fiber optics, the relevant models can explain the propagation of soliton pulses through intercontinental distances. The dynamics of soliton propagation through nonlinear optics, optical fibers, metamaterials, and crystals are described by several model equations, such as the nonlinear unstable Schrödinger's equation [3], Sasa-Satsuma equation [4], complex Ginzburg-Landau equation [5], perturbed Gerdjikov-Ivanov equation [6], Lakshmanan-Posezian-Daniel equation [7,8], Chen-Lee-Liu equation [9][10][11], Liquid crystals equation [12] and several others. It is worth mentioning that some researchers have studied a number of various known models and investigated their corresponding soliton dynamics via diverse analytical methods, viz.…”

Section: Background and Literature Reviewmentioning

confidence: 99%

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

Kumar

Paul

Biswas

et al. 2020

Preprint

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This paper retrieves some new optical solutions to the Kundu-Mukherjee-Naskar (KMN) equation in the context of nonlinear optical fiber communication systems. In this regard, the generalized Kudryashov and new auxiliary equation methods are applied to the KMN equation and consequently, dark, bright, periodic U-shaped and singular soliton solutions are explored. The discrepancies between the present obtained solutions and the previously obtained solutions by using different methods are discussed. The time fractional derivative and an oblique wave transformation in coordination with the methods of interest are considered for acquiring new optical wave solutions of the KMN equation in the sense of conformable derivative and wave obliqueness, respectively. The effects of obliqueness and fractionality on the attained solutions are demonstrated graphically along with its physical descriptions. It is found that the optical wave phenomena are changed with the increase of obliqueness as well as fractionality. All the obtained optical solutions are found to be new in the sense of conformable derivative, wave obliqueness, and the applied methods. Finally, it is found that the utilized methods and the relevant transformation are powerful over the other methods and it can be applicable for further studies to explain the pragmatic phenomena in optical fiber communication systems.

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“…Since the LDP model plays a significant role in portraying several complex phenomena, many authors find and analysed the solution using analytical as well as numerical schemes. For instance, Arshed et al 54 find the optical solitons for the considered model with the help of exp-(ϕ(ξ))-expansion method in birefringent fibres; the bright optical solitons have been illustrated by Alqahtani et al 55 for LPD model using semi-inverse variational principle, the group invariant solutions, and optical solitons in optical fibres; and PCF is presented by Bansal et al, 56 the optical solitons in birefringent fibres for the considered model achieved by Ekici 57 using the extended Jacobi's elliptic function expansion method; Guzman et al 58 applied the method of undetermined coefficients in order to find the optical solitons with polarization mode dispersion for the considered complex non-linear problem; the singular and dark optical solitons are obtained by Javid and Raza 59 ; singular and dark optical solitons have been obtained by Jawad et al 60 ; and many others [61][62][63][64] presented some interesting results. However, these techniques have their one limitation like huge computation, perturbation, and discretization.…”

Section: Introductionmentioning

confidence: 99%

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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Optical solitons and group invariant solutions to Lakshmanan–Porsezian–Daniel model in optical fibers and PCF

Cited by 38 publications

References 9 publications

Solitary waves, shock waves and conservation laws with the surface tension effect in the Boussinesq equation

Solitary waves, shock waves and conservation laws with the surface tension effect in the Boussinesq equation

Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation

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

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