Article
Optics
Abdullah Sonmezoglu
Summary: In this paper, stationary optical solitons to nonlinear Schrodinger's equation with nonlinear chromatic dispersion and Kudryashov's quintuple power law nonlinearity are studied using the extended version of G'/G-expansion approach, resulting in various soliton solutions.
Article
Materials Science, Multidisciplinary
Farrah Ashraf, Tehsina Javeed, Romana Ashraf, Amina Rana, Ali Akgul, Shahram Rezapour, Muhammad Bilal Hafeez, Marek Krawczuk
Summary: In this paper, various integration schemes were used to obtain multiple solutions for Burger's equation and the Shallow water wave equation. The solutions were also presented graphically in different dimensions.
RESULTS IN PHYSICS
(2022)
Article
Optics
Hanaa A. Eldidamony, Hamdy M. Ahmed, Afaf S. Zaghrout, Youssra S. Ali, Ahmed H. Arnous
Summary: This article considers the nonlinear Schrodinger's equation with Kudryashov's quintuple power law of refractive index, and implements the modified extended direct algebraic algorithm to extract various types of solutions for this model. Different structures of solutions are listed and illustrated graphically, showcasing the versatility of the model.
Article
Engineering, Electrical & Electronic
Mehmet Ekici
Summary: The extended Jacobi's elliptic function approach is used in this paper to study optical solitons in the nonlinear Schrodinger's equation. This approach can recover various types of soliton solutions, including bright solitons, dark solitons, singular solitons, and dark-singular form of straddled solitons.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Optics
Mehmet Ekici
Summary: This paper investigates the recovery of stationary optical solitons using Kudryashov's recently proposed nonlinear refractive index structure with quintuple power laws. The extended Jacobi's elliptic function expansion is employed as the integration algorithm, considering both linear and generalized formats of the temporal evolution term.
JOURNAL OF NONLINEAR OPTICAL PHYSICS & MATERIALS
(2023)
Article
Physics, Applied
Nilkanta Das, S. Saha Ray
Summary: In this study, the extended Jacobi elliptic function expansion approach was used to analyze a generalized (3+1)-dimensional Gross-Pitaevskii equation with distributed time-dependent coefficients. The approach successfully obtained spatiotemporal soliton solutions and exact extended traveling-wave solutions. Several double periodic, trigonometric, and hyperbolic function solutions were found under specific constraints. The proposed approach is considered to be the most straightforward, efficient, and useful way to handle nonlinear models and generate various exact solutions. The acquired solutions are of considerable importance due to their applicability to a variety of quantum systems.
MODERN PHYSICS LETTERS B
(2023)
Article
Physics, Multidisciplinary
Anjan Biswas, Mehmet Ekici, Abdullah Sonmezoglu
Summary: This paper implements extended trial function algorithm to retrieve stationary optical soliton solutions to the governing nonlinear Schrodinger's equation with Kudryashov's lately proposed quintuple power law of refractive index, in the presence of nonlinear chromatic dispersion. Both, linear temporal evolution as well as generalized temporal evolution are taken into account.
Article
Mathematics, Interdisciplinary Applications
Wafaa B. Rabie, Hamdy M. Ahmed
Summary: This article considers the twin-core couplers with Kudryashov's sextic power law of refractive index and perturbation terms. The extended F-expansion method is used to construct cubic-quartic solitons in optical metamaterials and other solutions. Bright soliton solutions, singular soliton solutions, periodic solutions, and combo periodic solutions are obtained. Moreover, some of the obtained solutions are represented graphically for physical illustration.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics
Wafaa B. B. Rabie, Hamdy M. M. Ahmed, Walid Hamdy
Summary: This study investigates optical soliton solutions in a magneto-optical waveguide and other exact solutions for the coupled system of the nonlinear Biswas-Milovic equation with Kudryashov's law using the extended F-expansion method. Various types of solutions are obtained, including dark solitons, singular solitons, dark-singular combo solitons, singular combo soliton solutions, Jacobi elliptic solutions, periodic solutions, combo periodic solutions, hyperbolic solutions, rational solutions, exponential solutions, and Weierstrass solutions. These different types of wave solutions are useful for obtaining nonlinear optical fibers in the future. The method used in this study provides effective and direct mathematical tools for solving nonlinear problems in the field of nonlinear wave equations.
Article
Engineering, Electrical & Electronic
Maasoomah Sadaf, Ghazala Akram, Saima Arshed, Habiba Sabir
Summary: The aim of this study is to investigate the dynamical behavior of (1 + 1)-dimensional Kudryashov's equation with generalized anti-cubic nonlinearity and extract its exact closed form solitons and other traveling wave solutions. Two techniques, the general projective Riccati equation method and the Jacobi elliptic method, are used to retrieve the explicit solution expressions. The solutions include hyperbolic, trigonometric, and Jacobi elliptic functions, displaying kink, combo dark-bright, and dark solitons as well as periodic traveling wave solutions. Three-dimensional graphs and two-dimensional contour graphs are used to visualize the results.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Optics
Muhammad Shakeel, Aysha Bibi, Dean Chou, Asim Zafar
Summary: The main purpose of this article is to explore the analytic soliton solutions of a nonlinear Schrodinger equation (NLSE), including Kudryashova's quintuple power-law with dual form nonlinearity by presenting two efficient analytical techniques. The present equation is a significant model which deals with a variety of nonlinear phenomenons in the fields of optical fibers. Modified G' G2-expansion method and exp(-9(p)) method are used to explore various forms of soliton solutions, such as kink-singular, bright, dark and cupson-singular forms. These techniques produce rational, trigonometric solutions for the nonlinear partial differential equation and have not been applied to the present model before.
Article
Engineering, Multidisciplinary
Manar S. Ahmed, Afaf A. S. Zaghrout, Hamdy M. Ahmed
Summary: In this paper, the improved modified extended tanh-function method is used to obtain new exact traveling wave solutions for the doubly dispersive model. Various types of solutions, including bright solitons, dark solitons, bright-dark combo solitons, hyperbolic type solutions, singular periodic wave solutions, Jacobi elliptic function solutions, exponential solutions, and Weierstrass elliptic doubly periodic solutions, are obtained. Some of these solutions are reported for the first time, and 3D graphs are introduced to illustrate the physical interpretation.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Dilek Varol
Summary: This article introduces the improved Kawahara equation, which is one of the most significant nonlinear evolution equations in mathematical physics. The analytical solutions of the conformable fractional extended Kawahara equation were obtained using the Jacobi elliptic function expansion method. By changing variables, this extended equation can be applied to different fractional forms in time, space, or both. Various types of fractional problems are illustrated to demonstrate the practical application of the given method, and some of the obtained solutions are presented in two- or three-dimensional graphics as visual proof.
FRACTAL AND FRACTIONAL
(2023)
Article
Optics
Wafaa B. Rabie, Hamdy M. Ahmed
Summary: In this work, optical solitons of the nonlinear Biswas-Milovic equation with Kudryashov's law are obtained using the improved modified extended tanh-function method. Several optical solitons, including traveling wave solutions, are revealed. Various forms of solutions are identified, and constraint conditions for their existence are given, along with dimensional graphs for physical interpretation.
Article
Engineering, Electrical & Electronic
Khalid K. Ali, M. S. Mehanna, Mohamed S. Mohamed
Summary: The article aims to present the optical soliton solutions of the nonlinear Schrodinger equation, which have important applications in optical fiber and photonic crystal fiber. Two powerful analytical techniques, the Sardar-Subequation method and the New method (G'/kG'+G+r)-expansion method, are employed to provide diverse solutions. The majority of the results are depicted graphically.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
