Applications of three methods for obtaining optical soliton solutions for the Lakshmanan–Porsezian–Daniel model with Kerr law nonlinearity

Rezazadeh, Hadi; Kumar, Dipankar; Neirameh, Ahmad; Eslami, Mostafa; Mirzazadeh, Mohammad

doi:10.1007/s12043-019-1881-5

Cited by 60 publications

(18 citation statements)

References 43 publications

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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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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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“…G -expansion method [9][10][11], the Clarkson-Kruskal (CK) direct method [12], the modified Kudryashov method [13], adomian decomposition methods [14][15][16], [17], first integral method [18], collocation method [19], new sub equation method [20], residual power series method [21], homogeneous balance method [22] and so on [28][29][30][31][32][33][34][35][36][37]. Consider the KPP equation [23] where v,  and  are real numbers.…”

Section: 'mentioning

confidence: 99%

Kolmogorov – Petrovskii – Piskunov denkleminin analitik çözümleri

Durur

Yokuş

2020

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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In the current study, analytical solutions are constructed by applying (1 / ) G -expansion method to the Kolmogorov-Petrovskii-Piskunov (KPP) equation. Hyperbolic type exact solutions of the KPP equation are presented with the successfully applied method. 3D, 2D and contour graphics are presented by giving special values to the parameters in the solutions obtained. This article explores the applicability and effectiveness of this method on nonlinear evolution equations (NLEEs).

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“…A variety of powerful methods have been used to study the nonlinear evolution equations, for the analytic and numerical solutions. Some of these methods, the Riccati Equation method [1], Hirota's bilinear operators [2], exponential rational function method [3], the Jacobi elliptic function expansion [4], the homogeneous balance method [5], the tanh-function expansion [6], first integral method [7,8], the subequation method [9], the expfunction method [10], the Backlund transformation, and similarity reduction [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], are used to obtain the exact solutions of NLPDE.…”

Section: Introductionmentioning

confidence: 99%

Solitary Wave Solutions to the Multidimensional Landau–Lifshitz Equation

Neirameh

2021

Advances in Mathematical Physics

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In this paper, we study the different types of new soliton solutions to the Landau–Lifshitz equation with the aid of the auxiliary equation method. Then, we get some special soliton solutions for this equation. Without the Gilbert damping term, we present a travelling wave solution with a finite energy in the initial time. The parameters of the soliton envelope are obtained as a function of the dependent model coefficients.

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Applications of three methods for obtaining optical soliton solutions for the Lakshmanan–Porsezian–Daniel model with Kerr law nonlinearity

Cited by 60 publications

References 43 publications

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

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

Kolmogorov – Petrovskii – Piskunov denkleminin analitik çözümleri

Solitary Wave Solutions to the Multidimensional Landau–Lifshitz Equation

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