Article
Engineering, Multidisciplinary
Nivan M. Elsonbaty, Niveen M. Badra, Hamdy M. Ahmed, Ahmed M. Elsherbeny
Summary: This study investigates cubic-quartic optical solitons and other solutions for the Biswas-Milovic equation with dual-power law nonlinearity using the improved modified extended tanh-function method. Bright soliton solutions, dark soliton solutions, singular soliton solutions, singular periodic solutions, Jacobi elliptic solutions, and hyperbolic solutions are obtained. Additionally, selected solutions are graphically described to illustrate their physical properties.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Optics
Mustafa Bayram
Summary: This study aims to solve the (3+1) dimensional Biswas-Milovic equation and obtain bullet solutions for both the Kerr law and parabolic law nonlinearities. The originality lies in the use of new and classical methods to solve these equations, and the analysis of parameter effects using 2D, 3D, and contour graphics.
Article
Mathematics, Interdisciplinary Applications
Abdulwahab Almutairi
Summary: In this paper, we apply the unified solver approach and the exp(-phi(xi))-expansion method to construct various solitary wave solutions for the fractional Biswas-Milovic model using conformable fractional derivative. We also study stochastic modeling and determine statistical properties of the solutions, showing the robustness of the proposed techniques in solving nonlinear fractional order equations.
FRACTAL AND FRACTIONAL
(2022)
Article
Materials Science, Multidisciplinary
Renfei Luo, Neeraj Dhiman, Fakhroddin Nazari, Jamilu Sabi'u, Hijaz Ahmad, Phatiphat Thounthong, Thongchai Botmart
Summary: This paper introduces a new method to obtain explicit solutions of the Atangana conformable fractional Bis-was-Milovic equation, showcasing its advantages in dynamical performance and optical solitons.
RESULTS IN PHYSICS
(2022)
Article
Optics
Lanre Akinyemi
Summary: Abundant optical soliton solutions of the Biswas-Milovic equation with Kudryashov's law and nonlinear perturbation terms in polarization preserving fibers are constructed using two improved analytical schemes, and many constraint conditions emerge. These solutions include bright soliton, W-shaped soliton, dark soliton, etc., and have been verified through symbolic computations.
Article
Optics
Lakhveer Kaur, Abdul-Majid Wazwaz
Summary: This course of research focuses on the Biswas-Milovic (BM) model with variable coefficients, including the Kerr law and damping effect. The Biswas-Milovic (BM) equation provides a mathematical framework for describing soliton transmission via optical wave guides in a more general sense. By employing different ansatz techniques and time-dependent coefficients, bright, dark, and singular soliton solutions to the governing equation have been successfully obtained. The acquired solutions are presented through various appealing figures, reflecting the potential characteristics of such solitons.
Article
Optics
Elsayed M. E. Zayed, Reham M. A. Shohib, Mohamed E. M. Alngar, Taher A. Nofal, Khaled A. Gepreel, Yakup Yildlrim
Summary: This paper presents cubic-quartic optical solitons for the first time using a newly introduced governing model derived from the Biswas-Milovic equation. Two integration approaches are used to extract different types of solitons.
Article
Materials Science, Multidisciplinary
Li-Feng Guo, Wan-Rong Xu
Summary: This paper investigates the traveling wave solutions for nonlinear Biswas-Milovic equation in magneto-optical wave guide coupling system with Kudryashov's law of refractive index. Four stable modes are identified through topological stability and dynamic behavior analysis, with specific representations provided under certain parameters.
RESULTS IN PHYSICS
(2021)
Article
Optics
Selvi Altun, Muslum Ozisik, Aydin Secer, Mustafa Bayram
Summary: This study examines the optical soliton solutions of the nonlinear Schrodinger form of the (2+1)-Biswas-Milovic equation with Kerr, power, and parabolic law nonlinearity. The new Kudryashov method is used to derive soliton solutions, and it is found that these solutions have basic soliton shapes. This investigation of the (2+1)-Biswas-Milovic equation with Kerr, power, and parabolic law nonlinearity is presented for the first time in this manuscript.
Article
Optics
Elsayed M. E. Zayed, Reham M. A. Shohib, Mohamed E. M. Alngar
Summary: This paper presents dispersive optical solitons with Biswas-Milovic equation, showcasing dark solitons, bright solitons, singular solitons, combo-singular solitons, and combo bright-singular solitons through a new mapping approach and an addendum to Kudryashov's algorithm.
Article
Optics
Elsayed M. E. Zayed, Khaled A. Gepreel, Reham M. A. Shohib, Mohamed E. M. Alngar, Yakup Yildirim
Summary: This paper investigates optical solitons in the perturbed Biswas-Milovic equation describing pulse propagation in optical fiber. Hamiltonian perturbations of maximum intensity are considered, and solutions using Jacobi elliptic functions are found using the unified auxiliary equation method. Various types of solitons, including dark, singular, bright, combo singular, and combo dark-singular solitons, are obtained.
Article
Optics
Pinar Albayrak
Summary: The purpose of this scientific research is to examine the optical soliton solutions of the Biswas-Milovic equation, which plays an important role in nonlinear optic studies and still maintains its significance in the field. Two efficient methods, the Kudryashov and the new Kudryashov, have been utilized to obtain the soliton solutions from the nonlinear differential equation form. The findings show that different optical soliton solutions of the Biswas-Milovic equation with spatio-temporal dispersion have been successfully obtained.
Article
Mathematics, Applied
Lanre Akinyemi, Mohammad Mirzazadeh, Kamyar Hosseini
Summary: In this paper, we analytically study the exact solitary wave solutions of the perturbed nonlinear Biswas-Milovic equation with Kudryashov's law of refractive index. We apply three efficient and reliable schemes, namely the simple equation method, the (G'/G)-expansion method, and the new Kudryashov method. The obtained solutions include bright solitons, dark solitons, singular solitons, periodic, rational, and exponential solutions, which are also verified through symbolic computations.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2022)
Article
Optics
M. L. Rupa, K. Aruna
Summary: This article investigates the optical soliton solutions of the time fractional Biswas-Milovic equation using the Shehu Adomian Decomposition Method (SADM). Various fractional order models, including Caputo (C), Caputo-Fabrizio (CF), and Atangana-Baleanu in Caputo sense (ABC) derivatives, are employed for validation and comparison. The convergence and uniqueness of the proposed techniques are analyzed, and numerical simulations are conducted to compare with existing methods. Additionally, 2-D, 3-D, and contour graphs are presented to depict the behavior of the obtained solutions.
Article
Optics
Mohammad Mirzazadeh, Arzu Akbulut, Filiz Tascan, Lanre Akinyemi
Summary: Modeling the movement and propagation of waves is crucial in fluid dynamics. All types of wave phenomena have significant importance in practical applications. This study effectively solves the perturbed Biswas-Milovic equation with Kudryashov's law of refractive index using an efficient solver and an improved F-expansion approach, obtaining trigonometric, hyperbolic, and rational function solutions that are applicable to real-world problems in fluid dynamics, optical fibers, plasma physics, and more. Additionally,three-dimensional and contour graphs are used to illustrate the behavior of some obtained solutions.
Article
Engineering, Multidisciplinary
Jianguo Ren, Jalil Manafian, Muhannad A. Shallal, Hawraz N. Jabbar, Sizar A. Mohammed
Summary: This work investigates a new numerical solution for a well-known non-linear wave equation, using the quintic B-spline collocation method. The method is shown to be unconditionally stable and efficient, with results in good agreement with the analytic solution. Physical interpretations of the results are demonstrated graphically using symbolic computation.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Xiao Hong, Mahyuddin K. M. Nasution, Onur Alp Ilhan, Jalil Manafian, Mostafa Abotaleb
Summary: This study considers different optical soliton wave solutions for nonlinear Schrodinger's equations describing magnetic ordering in ferromagnetic materials and CDA waves in plasma physics. The equations are analyzed using an improved integration technique and their dynamic structure and physical properties are depicted using symbolic computation.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Engineering, Multidisciplinary
Junjie Li, Jalil Manafian, Nguyen Thi Hang, Dinh Tran Ngoc Huy, Alla Davidyants
Summary: This paper investigates various solutions of the generalized KP-BBM equation, including soliton solutions, stripe soliton solutions, periodic wave solutions, and cross-kink wave solutions. The exact solutions are obtained through the Hirota bilinear method and numerical calculations, and the dynamical characteristics and interaction behaviors of these solutions are analyzed in detail.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Physics, Applied
Guanqi Tao, Jalil Manafian, Onur Alp Ilhan, Syed Maqsood Zia, Latifa Agamalieva
Summary: This paper verifies and scans the (3+1)-dimensional variable-coefficient nonlinear wave equation, which is generated by considering the Hirota bilinear operators and considering soliton theory. By using Maple symbolic computations, some novel exact analytical solutions are obtained, including cross-kink soliton solutions, breather wave solutions, interaction between stripe and periodic waves, multi-wave solutions, periodic wave solutions, and solitary wave solutions. The analyticity and positivity of the solutions can be easily achieved by selecting specific parameters. The main contribution of this work is the recovery of the Hirota bilinear forms and their generalized equivalences. Graphical simulations of the exact solutions are also presented.
MODERN PHYSICS LETTERS B
(2022)
Article
Engineering, Multidisciplinary
Yongyi Gu, Jalil Manafian, Mustafa Z. Mahmoud, Sukaina Tuama Ghafel, Onur Alp Ilhan
Summary: This paper investigates the exact analytical solutions and solution methods for the generalized Schrodinger equation, focusing on its applications to nonlinear Schrodinger equations. Various types of solutions are obtained and represented graphically, and the stability of these solutions is discussed. The proposed methods have significant potential for solving other nonlinear partial differential equations in different scientific fields.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Engineering, Electrical & Electronic
LuYu Sun, Jalil Manafian, Onur Alp Ilhan, Mostafa Abotaleb, Atheer Y. Oudah, A. S. Prakaash
Summary: This article investigates the new exact solitary wave solutions for the generalized nonlinear Schrodinger equation with parabolic nonlinear law. These solutions are obtained using the improved function technique. Different forms of solutions are obtained based on the map between the considered equation and an auxiliary ODE.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Physics, Mathematical
Md Nur Alam, Onur Alp Ilhan, Jalil Manafian, Muhammad Imran Asjad, Hadi Rezazadeh, Haci Mehmet Baskonus
Summary: This article investigates the new results of three nonlinear conformable models and applies the generalized Kudryashov method to derive stable soliton structures that are applicable in various fields. The research outcomes demonstrate the significant value of this approach in studying nonlinear conformable order models in theoretical physics.
ADVANCES IN MATHEMATICAL PHYSICS
(2022)
Article
Mathematics, Applied
Yingfang Pan, Jalil Manafian, Subhiya M. Zeynalli, Riyadh Al-Obaidi, R. Sivaraman, Ammar Kadi
Summary: This paper investigates the (3+1)-dimensional variable-coefficient generalized nonlinear wave equation arising in a liquid with gas bubbles. Using the Hirota bilinear technique and binary bell polynomials, new analytic solutions, such as one-lump soliton, two-lump soliton, and three-lump soliton, are obtained and analyzed. The results are useful for obtaining and explaining some new soliton phenomena.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2022)
Article
Mathematics
Ruijuan Li, Onur Alp Ilhan, Jalil Manafian, Khaled H. Mahmoud, Mostafa Abotaleb, Ammar Kadi
Summary: In this paper, the exact solutions of the (3+1)-dimensional variable-coefficient generalized shallow water wave equation are studied using the Hirota bilinear method. Multiple rational solutions are obtained by selecting different interactions. The method shows progress in solving extended homoclinic breather wave solutions and presents the results in different graphical forms.
Article
Physics, Applied
Yongyi Gu, Jalil Manafian, Somaye Malmir, Baharak Eslami, Onur Alp Ilhan
Summary: In this paper, the authors analyze a (2+1)-dimensional Konopelchenko-Dubrovsky equation in fluid dynamics and obtain lump-trigonometric solutions and rogue waves using the Hirota bilinear form and Maple software. They also study the influence of parameters on the type of solutions, and introduce special rogue waves when the lump solution is cut by twin-solitons. Additionally, they obtain a new set of sufficient solutions containing breather wave, cross-kink, periodic-kink, multi-waves and solitary wave solutions. The findings in this study can serve as a basis for future research on the performance of the mentioned equation.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Materials Science, Multidisciplinary
Yongyi Gu, Syed Maqsood Zia, Mubeen Isam, Jalil Manafian, Afandiyeva Hajar, Mostafa Abotaleb
Summary: In this article, the generalized (2+1)-dimensional shallow water wave equation, which allows unidirectional propagation of shallow-water waves, is investigated. By exploiting the integrability of the system, various forms of solitary wave solutions are obtained using the rogue wave and semi-inverse variational principle (SIVP) schemes. Specifically, four solutions including rogue wave, soliton, bright soliton, dark soliton, and lump solutions are studied. An illustrative example of the Helmholtz equation is provided to demonstrate the feasibility and reliability of the used procedure in this study. The impact of free parameters on the behavior of the obtained solutions is also analyzed, considering the nonlinear nature of the system. The dynamic properties of the obtained results are visualized and analyzed using density, two-dimensional, and three-dimensional images, and the physical nature of the solutions is presented.
RESULTS IN PHYSICS
(2023)
Article
Physics, Applied
SiSheng Zhang, Jalil Manafian, Onur Alp Ilhan, Abduladheem Turki Jalil, Yaser Yasin, M. Abdulfadhil Gatea
Summary: In this paper, the cubic-quintic nonlinear Helmholtz equation is studied, which allows for a pulse with Kerr-like and quintic properties to have further spatial dispersion. Various forms of solitary wave solutions are obtained using a generalized G'=G-expansion method, considering the nonintegrable nature of the system. The four types of function solutions, including soliton, bright soliton, singular soliton, and periodic wave solutions, are investigated. The obtained solutions' dynamical properties are analyzed and demonstrated through density, two-dimensional, and three-dimensional plots.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Cheng Li, Jalil Manafian, Baharak Eslami, Khaled Hussein Mahmoud, Russul Reidh Abass, Bashar S. Bashar, Onur Alp Ilhan
Summary: This paper investigates the propagation of solitary polarization in thin-film ferroelectric materials through the thin-film ferroelectric material equation (TFFME) and nonlinear evolution equations. The effects of different formulas on the solutions are explored and analyzed. The results provide a way for future research on generating optical memories based on nonlinear solitons.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Dingsi Li, Jalil Manafian, Onur Alp Ilhan, Safa Alkhayyat, K. H. Mahmoud, Ali Alsalamy, Subhiya M. Zeynalli
Summary: In this paper, the integrability of the nonparaxial nonlinear Schrodinger equation is studied, which allows the propagation of ultra-broad nonparaxial beams in a planar optical waveguide. Numerous solitary wave solutions are found using Hirota's bilinear scheme, and the conversion of the nonlinear system to a bilinear form is explored. New approaches for recovering periodic wave, bright soliton, singular, and singular soliton are implemented. The recovered solitons are important for understanding the behavior of solitons in optical fiber. Graphical representations of important solutions are discussed to provide physical illustrations and insights into the equation's characteristics.
MODERN PHYSICS LETTERS B
(2023)
Article
Mathematics
Wensheng Chen, Jalil Manafian, Khaled Hussein Mahmoud, Abdullah Saad Alsubaie, Abdullah Aldurayhim, Alabed Alkader
Summary: This paper studies the Gilson-Pickering (GP) equation and its applications in plasma physics and crystal lattice theory. The model is explained, and various solutions are obtained using different techniques. The superiority and novelty of the new mathematical theory are demonstrated through theorems and examples.
