Bright solitons for twin-core couplers and multiple-core couplers having polynomial law of nonlinearity using Jacobi elliptic function expansion method

Khalil, Tarek A.; Badra, Niveen; Ahmed, Hamdy M.; Rabie, Wafaa B.

doi:10.1016/j.aej.2022.05.042

Cited by 16 publications

(2 citation statements)

References 21 publications

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“…This research field has attracted many scholars at home and abroad. With the continuous exploration of researchers, a series of methods have been explored, such as Newton s ¢ method [1], Darboux transformation approach [2], exp-function approach [3], the Kudryashov s ¢ method [4], the Hirota method [5], the first integral method [6], the Robust inverse scattering method [7], Lie group method [8], the Jacobi elliptic function expansion method [9]. As consequence of the above methods, different kinds of exact solutions are obtained, such as lump waves [10], multiple stripe waves [10,11], kink waves [12], periodic waves [13], breather waves [14] and so on.…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation

Ma,

Qi,

Deng

2024

Phys. Scr.

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In this article, we aim to study the dynamical behavior of the (3+1)-dimensional Jimbo- Miwa-like (JML) equation. By using different methods, different forms of solutions are ob- tained. At the same time, in the same method, we also study the influence of parameters on the solution by changing the values of parameters. Firstly, we use the bilinear method to obtain the Y -type and X-type soliton solutions. Secondly, using different test functions, we obtain the interaction phenomenon between the solutions, which is obtained by a lump so- lution and a kink wave solution or by a lump solution and multi-kink wave solutions. Lastly, on the basis of the study of the single lump solution, we have made a further exploration. We not only obtain the lump-periodic solution, which verifies the periodicity, but also obtain the lump-soliton solution. For the above wave solutions, we graphically describe their dynamical properties with MAPLE. It is worth mentioning that the content of our study is different from the existing research: we not only use different methods to study the solutions of the JML equation, but also use different parameter relations and different values of parameters to study the changes of solutions. At the same time, we also use different test functions to study the same form of wave solutions. It is intuitive to see the influence of the test func- tion on the dynamic behavior of the solution. In addition, our results not only enable us to understand the dynamic properties of such equations more intuitively, but also provide some ideas for researchers to facilitate more indepth exploration.

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Section: Introductionmentioning

confidence: 99%

Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation

Ma,

Qi,

Deng

2024

Phys. Scr.

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“…Using symbolic tools, several suitable and efficient techniques for finding the appropriate solutions to various NLEEs have been demonstrated. There are several effective techniques, such as the Hirota bilinear technique (HBT) 8 , 9 , the modified Sardar sub-equation technique 10 , 11 , the hyperbolic-function technique 12 , the amended -Gordon expansion technique 13 , 14 , the Jacobi’s elliptic expansion technique 15 , 16 , the modified Fan-sub expansions technique 17 , 18 , the modified Kudryashov technique 19 , the Khater method 20 , the modified simple equation technique 21 , the unified Riccati equation expansion technique 22 and so on 23 , 24 . The authors in 25 studied the dynamical structure of soliton solutions, bifurcation analysis, and quasi-periodic solution to the (2+ 1)-dimensional Konopelchenko-Dubrovsky (KD) model.…”

Section: Introductionmentioning

confidence: 99%

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Nadeem,

Islam,

Şenol

et al. 2024

Sci Rep

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In this study, we examine multiple perspectives on soliton solutions to the (3+1)-dimensional Boussinesq model by applying the unified Riccati equation expansion (UREE) approach. The Boussinesq model examines wave propagation in shallow water, which is derived from the fluid dynamics of a dynamical system. The UREE approach allows us to derive a range of distinct solutions, such as single, periodic, dark, and rational wave solutions. Furthermore, we present the bifurcation, chaotic, and sensitivity analysis of the proposed model. We use planar dynamical system theory to analyze the structure and characteristics of the system’s phase portraits. The current study depends on a dynamic structure that has novel and unexplored results for this model. In addition, we display the behaviors of associated physical models in 3-dimensional, density, and 2-dimensional graphical structures. Our findings demonstrate that the UREE technique is a valuable mathematical tool in engineering and applied mathematics for studying wave propagation in nonlinear evolution equations.

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Cubic-quartic optical solitons of the complex Ginzburg-Landau equation: A novel approach

Arnous,

Nofal,

Biswas

et al. 2023

Nonlinear Dyn

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Bright solitons for twin-core couplers and multiple-core couplers having polynomial law of nonlinearity using Jacobi elliptic function expansion method

Cited by 16 publications

References 21 publications

Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation

Soliton solutions and the interaction behaviour of the (3+1)-dimensional Jimbo-Miwa-like equation

The dynamical perspective of soliton solutions, bifurcation, chaotic and sensitivity analysis to the (3+1)-dimensional Boussinesq model

Cubic-quartic optical solitons of the complex Ginzburg-Landau equation: A novel approach

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