The closed-form soliton solutions of the time-fraction Phi-four and (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff model using the recent approach

Al-Amin, M.; Islam, M. Nurul; Matkan, A A

doi:10.1016/j.padiff.2022.100374

Cited by 4 publications

(2 citation statements)

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“…It is well known that the mentioned technique is a particular case of the transformed rational function procedure [37], and the adopted auxiliary equation (17) implies that 1 G satisfies another Riccati equation. Therefore, all presented solutions here can be obtained from a general class of solutions to the general Riccati equation introduced in [38].…”

Section: (1/g ) Scheme For the Fl Modelmentioning

confidence: 99%

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Novel dynamics of the Fokas-Lenells model in Birefringent fibers applying different integration algorithms

Jahan,

Ullah,

Harun-Or-Roshid

et al. 2024

International Journal of Mathematics and Computer in Engineering

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The Fokas-Lenells model has the broad applications in nonlinear physics to study various soliton phenomena. Employing the direct algebraic scheme, the modified rational sine-cosine technique, and the (1/G′) expansion scheme, the analytical solutions to this model are derived. Double periodic waves, bright soliton, dark soliton, single and multiple breather waves, and periodic breather waves are extracted from this model using symbolic computation. The dynamic behaviors of the acquired outcomes are vividly illustrated through density, two-dimensional (2D), and three-dimensional (3D) graphical representations. These discoveries are strategically positioned to significantly contribute to the advancement of exploring nonlinear models, standing as a fundamental pillar for forthcoming research endeavors.

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Section: (1/g ) Scheme For the Fl Modelmentioning

confidence: 99%

“…Optical soliton disturbance is one of the most discernible bounds of exploration in the telecommunication industry [1][2][3][4][5][6]. The realm of studying soliton transmission in optical fibers has flourished in the last few decades due to its rich prominence of occurrences explaining these events [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Novel dynamics of the Fokas-Lenells model in Birefringent fibers applying different integration algorithms

Jahan,

Ullah,

Harun-Or-Roshid

et al. 2024

International Journal of Mathematics and Computer in Engineering

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Exploring the wave solutions of a nonlinear non-local fractional model for ocean waves

et al. 2023

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In this research, analytical and semi-analytical soliton solutions for the nonlinear fractional (2 + 1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation (FCBSE) in the non-local form are obtained using recent computational and numerical methods. The FCBSE is a significant model for investigating various phenomena, such as internal ocean waves, tsunamis, river tidal waves, and magneto-sound waves in plasma. The constructed solution helps in understanding the interaction between a long wave moving along the x-axis and a Riemann wave propagating along the y-axis. Various analytical solutions, such as exponential, trigonometric, and hyperbolic, have been formulated differently for this model, which is a specific derivation of the well-known Korteweg–de Vries equation. Density charts in two and three dimensions are used to visualize the behavior of a single soliton in reality through simulations. The results demonstrate the effectiveness of the employed numerical scheme and various methods to ensure the consistency of computational and approximation answers. Overall, this study demonstrates the potential of recent computational and numerical techniques for solving nonlinear mathematical and physical problems.

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Dynamical behavior of soliton solutions to the fractional phi-four model via two analytical techniques

Ahmad,

Younas

2024

Mod. Phys. Lett. B

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This study explores solutions for a mathematical equation called the time-space fractional phi-four equation using two methods: the Sardar-subequation method and the modified extended auxiliary equation method. The phi-four equation is connected to the Klein–Gordon model and is important in different scientific areas like biology and nuclear physics. Understanding its solutions is crucial. By using a specific wave transformation, the equation is changed into a simpler form for analysis. The methods proposed give a variety of solutions, such as Kink, bright singular, dark, combo dark bright, periodic, and singular periodic solutions. Each solution we find using these methods has specific rules that determine when it’s correct. We carefully choose specific values for the parameters to help us understand more about the solutions. This helps us see the detailed features of the solutions and improves our understanding of how the model behaves in the real world. These methods create a strong framework for studying solitons, which are specific types of mathematical solutions. The study compares the outcomes of these methods with earlier ones to get a complete understanding. Graphical illustrations are used to visually represent some of these solutions, helping us grasp their characteristics. Visual representations in two- and three-dimensional figures add originality to the findings. Importantly, these methods can be applied to solve similar problems with fractional derivatives in various scientific contexts. In summary, this research not only deepens our understanding of the phi-four equation but also introduces powerful methods with broad applications in fractional differential equations.

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The closed-form soliton solutions of the time-fraction Phi-four and (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff model using the recent approach

Cited by 4 publications

References 44 publications

Novel dynamics of the Fokas-Lenells model in Birefringent fibers applying different integration algorithms

Novel dynamics of the Fokas-Lenells model in Birefringent fibers applying different integration algorithms

Exploring the wave solutions of a nonlinear non-local fractional model for ocean waves

Dynamical behavior of soliton solutions to the fractional phi-four model via two analytical techniques

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