Sequel to “cubic‐quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov's method”

Arnous, Ahmed H.; Biswas, Anjan; Kara, A. H.; Milović, Daniela; Yıldırım, Yakup; Alshehri, Hashim M.

doi:10.1049/ote2.12065

Cited by 6 publications

(2 citation statements)

References 34 publications

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“…The pole value of the general solution is p = 4. Taking into account this value, we look for the solution of Equation ( 16) of the form (see [40][41][42][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68])…”

Section: Application Of the Simplest Equation Methods For Finding Exa...mentioning

confidence: 99%

Painlevé Test, Phase Plane Analysis and Analytical Solutions of the Chavy–Waddy–Kolokolnikov Model for the Description of Bacterial Colonies

Kudryashov

Лаврова

2023

Mathematics

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The Chavy–Waddy–Kolokolnikov model for the description of bacterial colonies is considered. In order to establish if the mathematical model is integrable, the Painlevé test is conducted for the nonlinear ordinary differential equation which corresponds to the fourth-order partial differential equation. The restrictions on the mathematical model parameters for ordinary differential equations to pass the Painlevé test are obtained. It is determined that the method of the inverse scattering transform does not solve the Cauchy problem for the original mathematical model, since the corresponding nonlinear ordinary differential equation passes the Painlevé test only when its solution is stationary. In the case of the stationary solution, the first integral of the equation is obtained, which makes it possible to represent the general solution in the quadrature form. The stability of the stationary points of the investigated mathematical model is carried out and their classification is proposed. Periodic and solitary stationary solutions of the Chavy–Waddy–Kolokolnikov model are constructed for various parameter values. To build analytical solutions, the method of the simplest equations is also used. The solutions, obtained in the form of a truncated expansion in powers of the logistic function, are represented as a closed formula using the formula for the Newton binomial.

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Section: Application Of the Simplest Equation Methods For Finding Exa...mentioning

confidence: 99%

Painlevé Test, Phase Plane Analysis and Analytical Solutions of the Chavy–Waddy–Kolokolnikov Model for the Description of Bacterial Colonies

Kudryashov

Лаврова

2023

Mathematics

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“…Moreover, these research and developments have also led to the emergence of some special and important new fields of study. Such as optics, optical soliton dynamics in fiber, optoelectronics etc [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

(2+1)-boyutlu kompleks lineer olmayan üç bağlı Maccari modelinin modifiye edilmiş yeni Kudryashov yöntemi ile topolojik olmayan soliton çözümü

Özişik

Tekercioglu

2022

EJOSAT

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This paper, deals with the (2+1)-dimensional complex three coupled nonlinear Maccari’s model (3-CCME) by utilizing recently presented modified new Kudryashov method (mNKM). The focus of this article is to obtain non-topological soliton solution of 3-CCME by applying mKNM method, which has not been applied before to the investigated problem. Applying the proposed method successfully, besides the non-topological soliton solution of the investigated problem, the breather-like type soliton solution was also obtained and the obtained results are depicted by the 3D, 2D and contour graphical presentations.

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Exact solutions of equation for description of embedded solitons

Kudryashov

2022

Optik

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Sequel to “cubic‐quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov's method”

Cited by 6 publications

References 34 publications

Painlevé Test, Phase Plane Analysis and Analytical Solutions of the Chavy–Waddy–Kolokolnikov Model for the Description of Bacterial Colonies

Painlevé Test, Phase Plane Analysis and Analytical Solutions of the Chavy–Waddy–Kolokolnikov Model for the Description of Bacterial Colonies

(2+1)-boyutlu kompleks lineer olmayan üç bağlı Maccari modelinin modifiye edilmiş yeni Kudryashov yöntemi ile topolojik olmayan soliton çözümü

Exact solutions of equation for description of embedded solitons

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