Optical soliton perturbation for Radhakrishnan–Kundu–Lakshmanan equation with a couple of integration schemes

Biswas, Anjan; Yıldırım, Yakup; Yaşar, Emrullah; Mahmood, Mohammad F.; Alshomrani, Ali Saleh; Zhou, Qin; Moshokoa, Seithuti P.; Belić, Milivoj R.

doi:10.1016/j.ijleo.2018.02.109

Cited by 137 publications

(23 citation statements)

References 9 publications

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“…(9). When we compare our results with the results reported in [40][41][42][43][44][45][46][47], we observed that, all the results obtained in this study by using the above method are newly structured solutions. These soliton solutions are located throughout parameter restrictions that provide their existence and novel soliton, traveling waves and kink-type solutions with complex structures while other solutions that emerged from the Laplace-Adomian decomposition method, traveling wave hypothesis, extended trial function scheme, among others.…”

Section: Resultssupporting

confidence: 59%

“…The work of [43] is devoted to extract some optical soliton solutions to the model with Kerr and power laws of nonlinearity by means of extended trial function scheme. Bright, dark and singular soliton solutions of the model with two types of Kerr and power law nonlinearities are derived in [44]. Their study is based on trial equation method and modified simple equation method.…”

Section: V)mentioning

confidence: 99%

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The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

Ghanbari

Gómez-Aguilar

2019

Rev. Mex. Fís.

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In this paper, the generalized exponential rational function method (GERFM) and the extended sinh-Gordon equation expansion method (ShGEEM) are used to construct exact solutions of the perturbed β-conformable-time Radhakrishnan-Kundu-Lakshmanan (RKL) equation. This model governs soliton propagation dynamics through a polarization-preserving fiber. Fractional derivatives are described in the β-conformable sense. As a result, we get new form of solitary traveling wave solutions for this model including novel soliton, traveling waves and kink-type solutions with complex structures. Physical interpretations of some extracted solutions are also included through taking suitable values of parameters and derivative order in them. It is proved that these methods are powerful, efficient, and can be fruitfully implemented to establish new solutions of nonlinear conformable-time partial differential equations applied in mathematical physics.

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Section: Resultssupporting

confidence: 59%

Section: V)mentioning

confidence: 99%

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

Ghanbari

Gómez-Aguilar

2019

Rev. Mex. Fís.

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“…Now if we combine the above constraints with (3.4), and substituting into (3.2), and the solutions Set [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] of (2.4), we obtain the following seventeen valid exact soliton solutions of (3.1), kx+wt+ε) , where w, L 0 and L 1 come from (3.5). There is a note that the solutions V 1,9 (x, t) and V 1,10 (x, t) are invalid for the constraints.…”

Section: Application Of the Tan( /2) Methods To The First Structure O...mentioning

confidence: 99%

Optical soliton solutions of the Biswas-Arshed model by the $\tan ( \circleddash /2)$ expansion approach

Hoque

Roshid

2020

Phys. Scr.

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In this paper, we consider the Biswas-Arshed model (BAM) with nonlinear Kerr and power law. We integrate these nonlinear structures of the BAM to obtain optical exact solitons that passing through the optical fibers. To retrieve the solutions, we apply the tan(/2) expansion integral scheme to the structures of the BAM nonlinearity. The novel solutions present optical shock wave, double periodic optical solitons, interaction between optical periodic wave and optical solitons, and optical periodic and rogue waves for both structures of the model. It is shown that the amplitude of the periodic double solitons waves gradually increases and reached the highest peak at the moment of interaction, and it goes to diminish for a much larger time. In fact, we show that the amplitude of the wave for the interaction between periodic and optical solitons, gradually increases with beat phenomena. To the purpose, all these types of optical solitons can be frequently used to amplify or reduce waves for a certain hight. Moreover, we describe the physical phenomena of the solitons in graphically.

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“…The RKL with Kerr law nonlinearity is given below (Biswas et al 2018b;Ozkan et al 2020b;Rehman et al 2019b;Sulaiman et al 2018;Seadawy et al 2020b) where the dependent variable Θ(x, t) is complex-valued wave profile with two independent variables of x and t that represents spatio-temporal component, respectively. The first term characterizes temporal evolution whereas the parameters denotes group velocity dispersion (GVD) while, the coefficients is Kerr nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Highly dispersive optical solitons and other soluions for the Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique

et al. 2021

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In this article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan-Kundu-Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multipleoptical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations

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Optical soliton perturbation for Radhakrishnan–Kundu–Lakshmanan equation with a couple of integration schemes

Cited by 137 publications

References 9 publications

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with β-conformable time derivative

Optical soliton solutions of the Biswas-Arshed model by the $\tan ( \circleddash /2)$ expansion approach

Highly dispersive optical solitons and other soluions for the Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers by an efficient computational technique

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