On the optical soliton solutions of Kundu–Mukherjee–Naskar equation via two different analytical methods

Onder, Ismail; Seçer, Aydın; Özişik, M.N.; Bayram, Mustafa

doi:10.1016/j.ijleo.2022.168761

Cited by 60 publications

(17 citation statements)

References 49 publications

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“…Because of its wide application, investigation of the analytical and soliton solutions of the NLPDEs with integer or fractional order has been very popular among authors over the past few decades. Numerous techniques consisting of the analytical and numerical methods have been improved to gain the soliton and analytical solutions of the PDEs such as the combined improved Kudryashov-new extended auxiliary sub equation method [1], the enhanced modified extended tanh-expansion approach [2,3], the sine-Gordon equation approach [4], F-expansion method [5], the tanh-coth function, the modified kudryashov expansion and rational sine-cosine approaches [6], the Riccati equation method [7], the tan(Θ/2) expansion approach [8], the Jacobi elliptic functions methodology [9], the generalized Bernoulli sub-ODE scheme [10], the extended ( G ′ G 2 )-expansion scheme [11], Nucci's reduction method [12], the new Kudryashov method [13][14][15], the sub-equation method based on Riccati equation [16], and the modified Sardar subequation method [17].…”

Section: Introductionmentioning

confidence: 99%

M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation

Özdemir

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This article aims to examine M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation (FE), which is a generalization of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations. The fractional (4+1)$-dimensional Fokas equation with the M-truncated derivatives is also studied first time in this study. The generalized projective Riccati equations method (GPREM) is successfully implemented. In the application of the presented method, a suitable fractional wave transformation is chosen to convert the proposed model into a nonlinear ordinary differential equation. Then, a linear equation system is acquired utilizing the GPREM, the system is solved, and the suitable solution sets are obtained. Dark and singular soliton solutions are successfully derived. Under the selection of appropriate values of the parameters, 2D, 3D, and contour plots are also displayed for some solutions.

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Section: Introductionmentioning

confidence: 99%

M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation

Özdemir

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…have been developed for both numerical and symbolic programming and thus great progress has been made in solving many non-linear problems waiting to be solved before. Many researchers started to work in this field and developed new equations (for example, Kadomtsev Petviasvili (KP) and its variants, Kdv forms, Boussinessq forms, Maccari systems, Kawahara [11][12][13][14][15][16][17][18][19][20]. The equations listed above reflect only a fraction of the equations developed in this field and studied by many researchers.…”

Section: Introductionmentioning

confidence: 99%

Solitary wave solutions of the (4+1)-dimensional Fokas equation via an efficient integration technique

Albayrak

2023

EJOSAT

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In this study, the soliton solutions of the integrable nonlinear (4+1)-dimensional Fokas equation, which has a unique importance in high-dimensional problems, are examined by the new Kudryashov method, which has recently been introduced into literature. In addition to obtaining the basic soliton solutions of the (4+1)-dimensional Fokas equation, it is showed that the method can be easily used effectively for high-dimensional problems and is also reliable. 3D, 2D and contour presentations of the graphs of the soliton solutions obtained in the study were made and the necessary explanations were also made.

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“…Besides, there are some optical phenomena equations which models transmission on fibers or optical media. Namely, Kundu-Mukherjee-Naskar equation [14], Lakshmanan-Porsezian-Daniel equation [15], Ginzburg-Landau equation [16], Gerdjikov-Ivanov equation [17], Biswas-Milovic equation [18], Chen-Lee-Liu equation [19] and Fokas-Lenells equation [20]. Now back to our own work, we have reviewed all the details of the cubic-quartic Fokas-Lenells equation (CQFLE) which is a type of Fokas-Lenells equation (FLE).…”

Section: Introductionmentioning

confidence: 99%

Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

et al. 2022

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In this study, we have focused on finding soliton solutions of the cubic-quartic Fokas-Lenells equation, which models the nonlinear pulse transmission through optical fiber, is a pretty new and updated model. We have used three different efficient analytical methods, namely, the Sinh-Gordon expansion method, enhanced modified extended tanh expansion method and unified Riccati equation expansion method. By modifying our proposed method and using it effectively, we have obtained much more optical solutions. We have supported the results with the 3D surface, 2D and contour plots of the soliton solutions, such as singular, periodic, periodic-singular, dark and M-shaped solitons. The originality of the method we propose is that it has never been used before. With the innovation of the method, we have obtained M-shaped solitons, which are very rarely obtainable in soliton waves. On the other hand, enhanced modified extended tanh expansion method have provided us more extra solutions. As the last and most important part, in order to examine physical behaviors, we have investigated the effect of the coefficient of the fourth order dispersion parameter on wave propagation by presenting the graphical representation.

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On the optical soliton solutions of Kundu–Mukherjee–Naskar equation via two different analytical methods

Cited by 60 publications

References 49 publications

M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation

M-truncated soliton solutions of the fractional (4+1)-dimensional Fokas equation

Solitary wave solutions of the (4+1)-dimensional Fokas equation via an efficient integration technique

Obtaining optical soliton solutions of the cubic–quartic Fokas–Lenells equation via three different analytical methods

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