Exact Solutions of the Two Dimensional KdV-Burger Equation by Generalized Kudryashov Method

Pandır, Yusuf; Eren, Sahragül

doi:10.21597/jist.713556

Cited by 7 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…applying generalized Kudryashov technique [13], exact solitons of KdV-Burger model are obtained in [14] etc.…”

Section: Of 23mentioning

confidence: 99%

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

Zafar,

Abukhaled,

Raheel

et al. 2023

Preprint

View full text Add to dashboard Cite

In this paper, new types of M-fractional wave solutions of mathematical physics model named as truncated M-fractional (1+1)-dimensional non-linear simplified Modified Camassa-Holm model are achieved by applying the modified simplest equation (MSE), Sardar sub-equation and generalized Kudryashov techniques. The gained solutions containing dark, bright, periodic and mixed wave solitons. Effect of fractional order derivative is also discussed. Achieved wave solitons are verified by Mathematica tool. Few of the gained wave solitons are also described through 2-dimensional, 3-dimensional and contour graphs through Mathematica tool. The gained solutions are helpful for the further development of concerned model. Finally, these techniques are simple, fruitful and effective to deal with non-linear FPDEs.

show abstract

“…applying generalized Kudryashov technique [13], exact solitons of KdV-Burger model are obtained in [14] etc.…”

Section: Of 23mentioning

confidence: 99%

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

Zafar,

Abukhaled,

Raheel

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In this study, GKM, which is one of the solution methods of NLEEs, is discussed (Tuluce Demiray, 2020; Tuluce Demiray and Bayrakci, 2021;Pandır and Eren, 2021;Kaplan and Akbulut, 2021;Gurefe, 2020;Islam et al 2019). Firstly, the structure of the method is introduced.…”

Section:  −mentioning

confidence: 99%

New Soliton Solutions Arising in Some NLEEs

BAYRAKCI

Demiray

Yildirim

2022

Bitlis Eren University Journal of Science and Technology

View full text Add to dashboard Cite

We have worked on (2+1)-dimensional dissipative long wave system (DLWS) and (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation. We have applied GKM, which has been obtained by generalizing the Kudryashov method, to the (2+1)- dimensional DLWS and (2+1)-dimensional DJKM equation. Thus, we have got some new soliton solutions of handled system and equation. We have plotted 2D and 3D surfaces of these acquired results by using Wolfram Mathematica 12. Then, we have shown the validity of the acquired solutions.

show abstract

“…New kinds of analytical wave solutions of three coupled nonlinear Maccari's system were obtained by the use of the extended sinh-Gordon equation expansion scheme [23]. Similarly, different types of exact soliton solutions of the fractional Sharma-Tasso-Olver (STO) equation and the fractional Bogoyavlenskii's breaking soliton equations were found using a generalized Kudryashov method in [24], optical and other types of solitons for different partial differential equations were obtained using this method in [25], some new kinds of exact wave solutions of the Burgers-type fractional space-time differential equations were calculated with the use of a generalized Kudryashov technique in [26], the bell, anti-bell, dark, kink, flat kink and other wave solutions of Fokas-Lenelles were obtained by applying a generalized Kudryashov technique in [27], and exact solitons of the Kudryashov-Burger model were obtained in [28].…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes

Zafar,

Raheel,

Ali

et al. 2023

Symmetry

View full text Add to dashboard Cite

This article concerns new analytical wave solutions of the Kuralay-II equations (K-IIAE and K-IIBE) with exploration of a new definition of the derivative. This model is used in various fields, like nonlinear optics, ferromagnetic materials and optical fibers. For this purpose, the expa function, the extended sinh-Gordon equation expansion scheme, and the generalized Kudryashov schemes were utilized. The resulting solutions are dark, bright, dark-bright, periodic, singular and other kinds of solitons. These results are obtained and also verified by the Mathematica tool. Some of the solutions are explained with 2-D, 3-D and contour plots using the Mathematica tool. The solutions obtained succede the present solutions in the literature. For the first time, the effect of the fractional derivative on the solutions is also shown graphically for this model. The analytical wave solutions are highly desirable as they offer insights into the underlying physics or mathematics of a system and provide a framework for further analysis. The results obtained can also be fruitful for the development of models in the future. The schemes used in this research are effective, easy to apply, and reliably handle other fractional non-linear partial differential equations.

show abstract

Exact Solutions of the Two Dimensional KdV-Burger Equation by Generalized Kudryashov Method

Cited by 7 publications

References 29 publications

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

New Types Of M-fractional Wave Solitons To The Mathematical Physics Model By Three Distinct Techniques

New Soliton Solutions Arising in Some NLEEs

Exact Solutions of M-Fractional Kuralay Equation via Three Analytical Schemes

Contact Info

Product

Resources

About