New $\phi^{6}$ ϕ 6 -model expansion method and its applications to the resonant nonlinear Schrödinger equation with parabolic law nonlinearity

Zayed, Elsayed M.E.; Al-Nowehy, Abdul-Ghani; Elshater, Mona E. M.

doi:10.1140/epjp/i2018-12288-2

Cited by 50 publications

(18 citation statements)

References 46 publications

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“…According to Zayed et al [28] the following are the key steps of a recent ϕ 6 -model expansion method:…”

Section: Description Of the Methodsmentioning

confidence: 99%

“…Step-5: According to [28], it is well known that the Jacobi elliptic solutions of Eq. ( 15) can be calculated when 0 < m < 1.…”

Section: Description Of the Methodsmentioning

confidence: 99%

“…® Received: 06.07.2022 ® Revised: 07.09.2022 ® Accepted: 14.09.2022 ® Published: 16.09.2022 the ϕ 6 -model expansion method [25,26,27,28], the nonstandard finite difference [29]. The recent developments in the field of mathematical modelling as well as its applications have been introduced in the last few decades [30,31,32].…”

Section: Introductionmentioning

confidence: 99%

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The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

Isah

Yokuş

2022

mmnsa

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This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor. The ϕ 6 -model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model. The results presented in this study are intended to improve the CGLE's nonlinear dynamical characteristics, it might also assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while the hyperbolic cotangent appears in the Langevin function for magnetic polarization. The current research is frequently used to report a variety of fascinating physical phenomena, such as the Kerr law of non-linearity, which results from the fact that an external electric field causes non-harmonic motion of electrons bound in molecules, which causes nonlinear responses in a light wave in an optical fiber. The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.

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“…According to Zayed et al [28] the following are the key steps of a recent ϕ 6 -model expansion method:…”

Section: Description Of the Methodsmentioning

confidence: 99%

“…Step-5: According to [28], it is well known that the Jacobi elliptic solutions of Eq. ( 15) can be calculated when 0 < m < 1.…”

Section: Description Of the Methodsmentioning

confidence: 99%

See 1 more Smart Citation

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

Isah

Yokuş

2022

mmnsa

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“…According to [31][32][33][34], the steps involves for the ϕ 6 -model expansion technique are given as:…”

Section: Description Of the Methodsmentioning

confidence: 99%

“…al, the first integral method [24,25], the hyperbolic trigonometric and rational function solutions are retrieved via the G ′ G −expansion approach [26] by Reza, the Lie point transformation method [27], Aminah used the sine-cosine function method [28] to construct the trigonometric wave solutions, Higazy et al implement the extended simple equation method [29] to get solitary wave solutions, the Modified simple equation method and Exp-function method [30] are used to obtain dark, trigonometric and hyperbolic soliton solutions. The Zoomeron model is studied in this research using the newly developed ϕ 6 -model expansion method [31][32][33][34]), which results in the restoration of optical solitary wave solutions.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons of Zoomeron equation by newly ϕ6-model expansion approach

Isah

Yokuş

2022

Preprint

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One of the equations describing incognito evolution, the nonlinear Zoomeron equation, is studied in this work. In a variety of physical circumstances, including laser physics, fluid dynamics and nonlinear optics, solitons with particular properties arise and the Zoomeron equation is a single example of one such situation. The Q^6-model expansion method allows for the explicit retrieval of a wide range of solution types, including kink-type solitons, these solitons are also called topological solitons in the context of water waves, their velocity does not depend on the wave amplitude, others are bright, singular, periodic and combined singular soliton solutions. The outcomes of this research may improve the Zoomeron equation's nonlinear dynamical features. The method proposes a practical and effective approach for solving a large class of nonlinear partial differential equations. Interesting graphs are employed to explain and highlight the dynamical aspects of the results, all of the obtained results are put into the Zoomeron equation to show the accuracy of the results.

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Dynamics of exact soliton solutions in the double‐chain model of deoxyribonucleic acid

Bilal

Younas

Ren

2021

Math Methods in App Sciences

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In this research, we study analytically the double‐chain model. The model consists of two long elastic homogeneous strands (or rods), which represent two polynucleotide chains of the deoxyribonucleic acid molecule, connected with each other by an elastic membrane (or some linear springs) representing the hydrogen bonds between the base pairs of the two chains. The new extended direct algebraic method and the generalized Kudryashov method are successfully utilized to discuss the exact soliton solutions to the double‐chain model of deoxyribonucleic acid that plays an important role in biology. The solutions obtained by these mechanisms can be divided into solitary, singular, kink, single wave, combine behavior as well as hyperbolic, plane wave, and trigonometric solutions with arbitrary parameters. Some solutions have been exemplified by graphics to understand the physical meaning of the DNA model. The accomplished solutions seem with all essential constraint conditions, which are obligatory for them to subsist. Hence, our techniques via fortification of symbolic computations provide an active and potent mathematical implement for solving diverse benevolent nonlinear wave problems. The results show that the system theoretically has extremely rich exact wave structures of biological relevance.

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New $\phi^{6}$ ϕ 6 -model expansion method and its applications to the resonant nonlinear Schrödinger equation with parabolic law nonlinearity

Cited by 50 publications

References 46 publications

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

Optical solitons of Zoomeron equation by newly ϕ6-model expansion approach

Dynamics of exact soliton solutions in the double‐chain model of deoxyribonucleic acid

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