Article
Optics
Ghazala Akram, Maasoomah Sadaf, Mirfa Dawood
Summary: This paper presents various soliton solutions of the Radhakrishnan-Kundu-Laksmanan (RKL) equation, including hyperbolic, trigonometric, rational, and exponential solutions obtained through an improved tan(Phi(xi)/2)-expansion technique. Graphical illustrations are provided to offer insights into the physical behavior of related phenomena.
Article
Physics, Multidisciplinary
Si-Yu Hong, Wei-Guo Zhang, Yu-Li Guo, Xing-Qian Ling
Summary: This paper mainly studies the orbital stability of the periodic traveling wave solution for the Eckhaus-Kundu equation with quintic nonlinearity. By constructing conserved quantities, conducting detailed spectral analysis, and employing appropriate techniques, the complexity of the equation is overcome, resulting in a conclusion on the orbital stability of the dn periodic wave solution.
Article
Engineering, Electrical & Electronic
Yesim Saglam Ozkan, Mostafa Eslami, Hadi Rezazadeh
Summary: In this paper, we utilized the improved tan(phi/2)-expansion method to construct exact solutions of the nonlinear Schrodinger equation modeling cubic optical solitons in a polarization-preserving fiber with Kerr law. The obtained solutions, including hyperbolic, trigonometric, exponential, and rational function solutions with free parameters, can be considered as a generalization of existing results in the ordinary derivative case. Geometrical shapes for some of the solutions were depicted for various choices of the free parameters, showcasing the novelty and versatility of the results.
OPTICAL AND QUANTUM ELECTRONICS
(2021)
Article
Mathematics, Applied
Mohammad Mohammadi, Rayhaneh Dehghani
Summary: This paper presents a comparative numerical study of the periodic phi(4) system and its different behaviors during collisions. Although the systems are similar for kink solutions, they exhibit differences in collisions, including critical velocities, outcomes, and rules in quasi-fractal structures. Three types of scattering windows are introduced based on speed, amplitude, and initial phase, with a detailed comparison of collisions between two kinks and one antikink at the end.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Engineering, Electrical & Electronic
Muhammad Bilal, Shafqat-Ur-Rehman, Jamshad Ahmad
Summary: In this study, the novel Phi (6)-model expansion method is used to solve the Kundu-Mukherjee-Naskar model of a nonlinear partial differential equation significant in optical fiber. Various nonlinear dynamical exact and optical solitons are extracted, including rational, hyperbolic, and trigonometric function solutions. Mixed combined solitons and singular periodic wave solutions with unknown parameters are also secured. Constraint conditions for validating the solutions are emerged, showing the rich optical solution structures of the governing model. Additionally, modulation instability analysis is conducted, and 3-D, 2-D, and corresponding contour plots are sketched under suitable parameter choices.
OPTICAL AND QUANTUM ELECTRONICS
(2021)
Article
Mathematics
Karim K. Ahmed, Niveen M. Badra, Hamdy M. Ahmed, Wafaa B. Rabie
Summary: Our paper studies optical solitons for the Kundu-Eckhaus equation with quintic nonlinearity and Raman effect. By applying the improved modified extended tanh-function method, various soliton solutions and their physical nature are obtained and illustrated graphically.
Retraction
Optics
Khalida Bibi
Summary: This paper applies the Phi(6)-model expansion method to derive new exact solutions for the perturbed Radhakrishnan-Kundu-Lakshmanan equation with Kerr law nonlinearity. The obtained solutions are based on Jacobi elliptic function, hyperbolic function, and trigonometric function solutions. Specific parameter values consistent with constraint conditions are assigned to reveal the dynamic behavior of the solutions.
Article
Mathematics
Shami A. M. Alsallami, Syed T. R. Rizvi, Aly R. Seadawy
Summary: We investigate the stochastic-fractional Drinfel'd-Sokolov-Wilson (SFDSW) equations for various wave solutions and interactions, including cross-kink rational waves, periodic cross-rational waves, homoclinic breather waves, M-shaped rational solutions, and M-shaped solutions with kink waves. These solutions have applications in mathematical physics, surface physics, plasma physics, population dynamics, and applied sciences. Graphical representations of the results are provided in different dimensions, obtained under certain constraint conditions.
Article
Materials Science, Multidisciplinary
T. R. Syed Rizvi, R. Aly Seadawy, M. Aamir Ashraf, Muhammad Younis, Abdul Khaliq, Dumitru Baleanu
Summary: In this paper, we aim to determine rogue-wave solutions for the Maccari-system and construct various unique solutions using exponential, rational, trigonometric functions, and bilinear forms. We also provide graphical representations of our results and explain their physical significance.
RESULTS IN PHYSICS
(2021)
Article
Engineering, Electrical & Electronic
Karim K. K. Ahmed, Niveen M. M. Badra, Hamdy M. M. Ahmed, Wafaa B. B. Rabie
Summary: This paper introduces the generalized Kundu-Eckhaus equation (KEE) with extra-dispersion, which describes the propagation of ultra-short femtosecond pulses in an optical fiber. Many exact solutions are constructed using the improved modified extended tanh-function method and a new transformation. As a result, a variety of new families of exact traveling wave solutions are found, including bright solitons, dark solitons, singular solitons, Weierstrass elliptic doubly periodic solutions, Jacobi elliptic solutions, periodic solutions, and rational solutions. Physical interpretation for some of the obtained solutions are illustrated in Figures.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Physics, Multidisciplinary
Dianchen Lu, Aly R. Seadawy, Muhammad Arshad
Summary: In this paper, four mathematical methods were employed to obtain exact solutions of the Kundu-Eckhaus equation in various forms, including bright and dark solitons, periodic solitary wave, etc. The results were graphically presented and show potential practical applications.
INDIAN JOURNAL OF PHYSICS
(2021)
Article
Physics, Multidisciplinary
Kang-Jia Wang, Hong-Wei Zhu
Summary: The paper investigates the application of the Kundu-Mukherjee-Naskar equation in optical soliton dynamics in (2 + 1) dimensions and successfully finds its periodic wave solution using the Hamiltonian-based algorithm. The proposed method demonstrates a good agreement with existing results, confirming its correctness. Numerical results are presented in the form of 3-D and 2-D plots, providing new insights for the study of periodic wave solutions.
Article
Materials Science, Multidisciplinary
Faiqa Ali, Adil Jhangeer, Muhammad Muddassar, Hassan Almusawa
Summary: This paper examines the various dynamic behaviors of the dispersive extended nonlinear Schrodinger equation using a new Phi(6)-model expansion method. The study focuses on exploring the solitary waves of the model and the impact of different parameters on Jacobian elliptic solutions. It also investigates phenomena such as bright-dark optical solitons and the transformation of the system into a planar dynamical system through Galilean transformation.
RESULTS IN PHYSICS
(2021)
Article
Physics, Applied
S. Saha Ray, N. Das
Summary: This article investigates the space-time fractional perturbed nonlinear Schrodinger equation in nanofibers using the improved tan(phi(xi)/2) expansion method to discover new exact solutions. The obtained soliton solutions are illustrated in 3D graphs to observe their behavior, indicating the proficiency of the proposed method in analyzing nonlinear partial differential models.
MODERN PHYSICS LETTERS B
(2022)
Article
Engineering, Electrical & Electronic
M. Ali Akbar, Farah Aini Abdullah, Mst. Munny Khatun
Summary: The study focuses on fractional nonlinear evolution equations and their optical soliton solutions. An important fractional nonlinear evolution equation, the time-fractional Kundu-Eckhaus equation, was analyzed using the (G'/G,1/G)-expansion approach. Various novel soliton solutions, including kink solitons, compactons, periodic solitons, singular periodic solitons, and singular bell-shaped solitons, were obtained. The results suggest that this method can be applied to other significant fractional nonlinear evolution equations to find diverse and improved soliton solutions.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Mathematics, Applied
Behzad Nemati Saray, Mehrdad Lakestani, Mehdi Dehghan
Summary: The paper presents the design, analysis, and testing of the multiwavelets Galerkin method for solving the two-dimensional Burgers equation. By discretizing time using the Crank-Nicolson scheme, a PDE is obtained for each time step and then solved using the multiwavelets Galerkin method. The results demonstrate the effectiveness of the method by reducing the number of nonzero coefficients while maintaining the error within a certain range.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
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
Automation & Control Systems
Milad Saiery, Javad Katebi, Mehrdad Lakestani
Summary: This paper proposes a method to solve the time-varying system control problem using forward Riccati formulation and hybrid functions. The proposed method does not require advanced knowledge of system dynamics or assumption of future information of system matrices. Numerical control cases demonstrate that this method is applicable to both periodic and non-periodic systems, with less control effort and significant damping time.
INTERNATIONAL JOURNAL OF CONTROL
(2023)
Article
Physics, Applied
Wenjie Wu, Jalil Manafian, Khalid K. Ali, Seydi Battal Gazi Karakoc, Abbas H. Taqi, Muhannad A. Mahmoud
Summary: In this paper, numerical solutions for the 1D Benjamin-Bona-Mahony (BBM) equation and 2D coupled BBM system are obtained using Galerkin finite element technique. The proposed methods are validated through error norms evaluation and stability analysis, showing robustness and efficiency in solving linear and nonlinear PDEs.
INTERNATIONAL JOURNAL OF MODERN PHYSICS 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
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
Computer Science, Information Systems
F. Gholami Bahador, P. Mokhtary, M. Lakestani
Summary: In this work, a time-space fractional differential equation is proposed to remove mixed Poisson-Gaussian noise. The combination of fixed-and variable-order fractional derivatives allows for the preservation of high-and low-frequency components while eliminating noise. The model shows efficacy not only for mixed noise reduction but also for images degraded solely by Gaussian noise. Additionally, a stable discretization strategy is presented, and the results demonstrate the superiority of the scheme over earlier models, reducing the staircase effect and being applicable to electron microscopy and CT images.
INFORMATION SCIENCES
(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, Applied
Lafta Abed Dawod, Mehrdad Lakestani, Jalil Manafian
Summary: The shallow water wave equation in oceanography and atmospheric science is extended to (3+1) dimensions, and an illustrative example of the VC generalized shallow water wave equation is used to demonstrate the feasibility and reliability of the procedure. The Hirota bilinear method is shown to be important in obtaining various types of rational solutions, and the equation is transformed into the Hirota bilinear form. The method is found to be concise, simple, and straightforward, and reveals many new types of traveling-wave solutions.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(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.
Article
Mathematics, Applied
Samira Bonyadi, Yaghoub Mahmoudi, Mehrdad Lakestani, Mohammad Jahangiri Rad
Summary: The paper proposes a spectral method for solving space-time fractional PDEs with variable coefficients. The method combines the spectral shifted Jacobi collocation method with the shifted Jacobi operational matrix of fractional derivatives. Both temporal and spatial discretizations are investigated using the spectral collocation method. By applying the shifted Jacobi collocation method, the problem is reduced to a system of algebraic equations, simplifying the problem greatly. Numerical results are presented to validate the accuracy and effectiveness of the proposed procedure for space-time fractional PDEs.
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS
(2023)
Article
Multidisciplinary Sciences
Araz Noori Dalawi, Mehrdad Lakestani, Elmira Ashpazzadeh
Summary: In this research, a collocation method based on biorthogonal Hermite cubic spline functions is developed to solve a class of fractional optimal control problems using the Caputo-Fabrizio derivative operator. Dual bases for Hermite cubic spline functions are designed for the first time, and two direct and efficient algorithms are proposed to solve the problems. New operational matrices of the Caputo-Fabrizio fractional derivative are derived using Hermite cubic spline functions. Through the use of these matrices, the problems are reduced to systems of algebraic equations. Illustrative examples are provided to demonstrate the important features of the new algorithm.
IRANIAN JOURNAL OF SCIENCE
(2023)
