New optical solitons of perturbed nonlinear Schrödinger–Hirota equation with spatio-temporal dispersion

Akinyemi, Lanre; Rezazadeh, Hadi; Shi, Qiu-Hong; Khater, Mostafa M. A.; Ahmad, Harith; Jhangeer, Adil; Akbar, M. Ali

doi:10.1016/j.rinp.2021.104656

Cited by 73 publications

(13 citation statements)

References 46 publications

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“…where either E 1 or E 2 and P 1 or P 2 may be zero but both cannot be zero at the same time. By substituting equation (54) into (6), we arrive at a nonlinear algebraic system which gives following solution sets. Set 2-1:…”

Section: Case 2: V ′ � Cos H(v)mentioning

confidence: 99%

“…Kumar developed the generalized exponential rational function approach to discover traveling waves, kink waves, rational function, lump-type solitons, multi-solitons, hyperbolic function, and trigonometric solutions. Using the simplest equation approach, Inc et al discovered accurate analytic solutions for the (2 + 1)-dimensional Ito problem [1][2][3][4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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Pattern Formation of a Bubbly Fluid Mixture under the Effect of Thermodynamics via Kudryashov-Sinelshchikov Model

Abdel‐Aty

Raza

Batool

et al. 2022

Journal of Mathematics

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In this paper, new explicit wave solutions via liquid-gas bubbles are obtained for the fractional Kudryashov-Sinelshchikov (KS) equation under thermodynamic assumptions. A new fractional de nition is applied to get these solutions that are utilized to represent the phenomenon of pressure waves under thermodynamic conditions. Two analytical techniques are used to explore the model which is sinh-Gorden equation expansion and Riccati-Bernoulli Sub-ODE methods. ese approaches provide complex hyperbolic, hyperbolic, complex trigonometric, and trigonometric solutions for the fractional KS equation, particularly singular, combined singular, dark, bright, combined dark-bright, and other soliton solutions. Furthermore, acquired results are illustrated by 3D graphs for suitable parametric values that highlight the physical importance and dynamical behaviors of the equation. It is also demonstrated that the purposed approaches are powerful strategies for developing exact traveling wave solutions for a wide range of problems found in mathematical sciences.

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Section: Case 2: V ′ � Cos H(v)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pattern Formation of a Bubbly Fluid Mixture under the Effect of Thermodynamics via Kudryashov-Sinelshchikov Model

Abdel‐Aty

Raza

Batool

et al. 2022

Journal of Mathematics

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“…Over the last several decades, one of the most significant challenges has been the development of new methods to construct exact solutions for NLPD equations. In recent years, several new, more powerful, and effective approaches have been established to retrieve exact solutions of NLPD equations, the sine-Gordon expansion method [1][2][3][4], the (𝐺 ′ 𝐺 ⁄ )-expansion method [5][6][7][8], the Sardar sub-equation method [9][10][11][12], the Kudryashov method [13][14][15][16][17][18], and the exponential method [19][20][21][22][23][24][25], are examples to mention.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity

Hosseini¹,

Mirzazadeh

Akinyemi

et al. 2022

Opt Quant Electron

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The major goal of the present paper is to construct optical solitons of the Ginzburg-Landau (GL) equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors' knowledge, the results reported in the current study, classified as bright and kink solitons, are new and have been acquired for the first time.

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“…n [24], Hirota bilinear method with appropriate polynomial functions in bilinear forms, the one-order rogue waves solution and its existence condition were obtained. Different methods and techniques were used to solve nonlinear evolution equations; T anh and Exp-function [25,26], G G expansion [27], Darboux transformation [28], Kyrdiashov method, [29], Hirota-bilinear transformation [30], Lie symmetries of NLPDEs [31].Very recently different methods and techniques were introduced, among them, the first integral method, the improved q-homotopy perturbation method and the unified algebraic and auxiliary equation expansion methods [32][33][34][35][36][37][38][39][40][41]. Here, the unified method (UM) [42][43][44][45][46][47] is used in this paper.…”

Section: Introductionmentioning

confidence: 99%

Continuum Soliton Chain Analog to Heisenberg Spin Chain System. Modulation Stability and Spectral Characteristics

Abdel‐Gawad

2022

Int J Theor Phys

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The one-dimensional (1D) Heisenberg spin chain system (HSCS) allows to investigate anomalous features originating from strong quantum fluctuations, which become more significant than those in higher dimensions. A continuum model equation of the HSCS, based on the discrete model, was constructed in the literature. It is nonlinear Schrodinger equation (NLSE) with biquadratic dispersion and fifth degree nonlinearity. Rare research works were done in this area. Notably for deriving the exact solutions and investigate the physical phenomena produced. Our objective, here, is to obtain these solutions, which we think they are new. Further, an analog of the different geometric solutions structures to the known characteristics of HSCS is performed. The unified method is implemented to find the exact solutions of the continuum model equation. A variety of solutions are obtained where they are evaluated numerically and represented in graphs. In these graphs, it is remarked that the solutions exhibit soliton chain (or dense soliton chain).in an analog to spin chain. In the contour plots, they show different shapes of super lattices. Furthermore, complex chirped waves are observed. A significant result is that these solutions are bounded by −1/4 and 1/4, which can be relevant to the spins−1/2 and 1/2. The analysis of modulation stability is carried and it is found that there is a critical value for the dominant parameters, where below this value, modulation instability holds otherwise modulation stability occurs.For the spectral characteristics, it is shown that the wave number increases abruptly and decreases to an asymptotic state, while the frequency is monotonic increasing. The spectrum is periodic wave away from the origin, but near the origin it is soliton.

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New optical solitons of perturbed nonlinear Schrödinger–Hirota equation with spatio-temporal dispersion

Cited by 73 publications

References 46 publications

Pattern Formation of a Bubbly Fluid Mixture under the Effect of Thermodynamics via Kudryashov-Sinelshchikov Model

Pattern Formation of a Bubbly Fluid Mixture under the Effect of Thermodynamics via Kudryashov-Sinelshchikov Model

Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity

Continuum Soliton Chain Analog to Heisenberg Spin Chain System. Modulation Stability and Spectral Characteristics

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