Analysis of some new wave solutions of fractional order generalized Pochhammer-chree equation using exp-function method

Zulfiqar, Aniqa; Ahmad, Jamshad; Ul-Hassan, Qazi Mahmood

doi:10.1007/s11082-022-04141-5

Cited by 12 publications

(3 citation statements)

References 28 publications

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“…The EFM [16] proposed by Ji-Huan He and Xu-Hong Wu in 2006 provides us with a straightforward and effective method for obtaining generalized solitary wave solutions and periodic solutions of NLEEs. The method has been applied to many kinds of equations like the double sine-Gordon equation [17], Burger equations [18], Maccari's system [19], the Klein-Gordon equation [20], the combined KdV-mKdV equation [21], variant Boussinesq equations [22], the Broer-Kaup-Kupershmidt equations [23], variable-coefficient equations [24], high-dimensional equations, discrete equations and so on [25][26][27]. In 2009, Dai et al [28] generalized the EFM to solve stochastic equations.…”

Section: Introductionmentioning

confidence: 99%

Solving the Fornberg–Whitham Model Derived from Gilson–Pickering Equations by Analytical Methods

O’Regan,

Aderyani,

Saadati

et al. 2024

Axioms

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This paper focuses on obtaining traveling wave solutions of the Fornberg–Whitham model derived from Gilson–Pickering equations, which describe the prorogation of waves in crystal lattice theory and plasma physics by some analytical techniques, i.e., the exp-function method (EFM), the multi-exp function method (MEFM) and the multi hyperbolic tangent method (MHTM). We analyze and compare them to show that MEFM is the optimum method.

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Section: Introductionmentioning

confidence: 99%

Solving the Fornberg–Whitham Model Derived from Gilson–Pickering Equations by Analytical Methods

O’Regan,

Aderyani,

Saadati

et al. 2024

Axioms

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“…These NLPDEs solutions provide improved support for the physical structures. To acquire the precise solution for nonlinear physical models, several robust and efficient techniques [4,5], were established, and these techniques are the Hirota bilinear technique [6], the F-expansion technique [7], the sinh-Gordon function technique [8], the Darboux transformation technique [9], new ϕ 6 -model expansion approach [10], the modified extended tanh-function technique [11,12], the sin-cosine technique [13] and several others. More recently, several approaches have also been considered for various lump solutions [14,15].…”

Section: Introductionmentioning

confidence: 99%

Dynamical perspective of bifurcation analysis and soliton solutions to (1+1)-dimensional nonlinear perturbed Schrödinger model

Javed,

Ali,

Muhammad

2024

Preprint

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This work simulates the (1+1)-dimensional nonlinear perturbed Schrödinger model (NLPSM). This model has various applications in mathematical physics and engineering, including hydrodynamics, elastic media, nonlinear optical fiber communication, and plasma physics. There are two primary goals for the study. First, it seeks to find unique soliton solutions such as solitary, dark, periodic, and plane wave solutions that haven’t been found in the literature before using the modified Sardar sub-equation approach (MSSEA). Second, a novel approach to analysis called bifurcation analysis is used to investigate the dynamic behavior of the model. Physical compatibility findings are supported by density, 3-D, and 2-D illustrations made with parametric variables. The analysis shows that the approach used to quickly acquire complete and typical answers was successful. This approach works well for solving challenging problems in physics, engineering, mathematics and fiber optic phenomena.

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“…They are essential for understanding and predicting the behavior of complex systems in both natural and engineered environments. However, due to the inherent complexity of NLPDEs [1][2][3][4][5][6], finding exact solutions using a single technique is often challenging. To address this, several reliable methods have been proposed, for instance, the modified exp(−ϕ(ω))expansion function [7,8], the sin-Gordon-expansion [9], the G ′ G 2 -expansion function [10], the first integral approach [11], and the Hirota bilinear approach [12,13].…”

Section: Introductionmentioning

confidence: 99%

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

Mohammed,

Agarwal,

Brevik

et al. 2024

Symmetry

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Recently, nonlinear fractional models have become increasingly important for describing phenomena occurring in science and engineering fields, especially those including symmetric kernels. In the current article, we examine two reliable methods for solving fractional coupled nonlinear Schrödinger models. These methods are known as the Sardar-subequation technique (SSET) and the improved generalized tanh-function technique (IGTHFT). Numerous novel soliton solutions are computed using different formats, such as periodic, bell-shaped, dark, and combination single bright along with kink, periodic, and single soliton solutions. Additionally, single solitary wave, multi-wave, and periodic kink combined solutions are evaluated. The behavioral traits of the retrieved solutions are illustrated by certain distinctive two-dimensional, three-dimensional, and contour graphs. The results are encouraging, since they show that the suggested methods are trustworthy, consistent, and efficient in finding accurate solutions to the various challenging nonlinear problems that have recently surfaced in applied sciences, engineering, and nonlinear optics.

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Analysis of some new wave solutions of fractional order generalized Pochhammer-chree equation using exp-function method

Cited by 12 publications

References 28 publications

Solving the Fornberg–Whitham Model Derived from Gilson–Pickering Equations by Analytical Methods

Solving the Fornberg–Whitham Model Derived from Gilson–Pickering Equations by Analytical Methods

Dynamical perspective of bifurcation analysis and soliton solutions to (1+1)-dimensional nonlinear perturbed Schrödinger model

On Multiple-Type Wave Solutions for the Nonlinear Coupled Time-Fractional Schrödinger Model

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