Article
Optics
Syed Tahir Raza Rizvi, Sarfraz Ahmad, M. Faisal Nadeem, Muhammad Awais
Summary: In this paper, optical solitons and other solitary wave solutions for (2+1)-dimensional nonlinear Schrodinger equation (NLSE) are obtained using extended modified auxiliary equation mapping method with cubic-quintic-septic nonlinearity. Bright, dark, singular, rational, periodic and many other solitary wave solutions are obtained for the governing model with constraint conditions.
Article
Engineering, Electrical & Electronic
Syed T. R. Rizvi, Aly R. Seadawy, S. Oan Abbas, Komal Naz
Summary: This paper studies two different nonlinear models: the Atangana-Baleanu fractional system of equations for the ion sound and Langmuir waves (ISALWs), and the Hirota Ramani equation. By solving these models, various solitary wave solutions of different types are obtained. The effectiveness of the solutions is verified through graphical representation.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Engineering, Electrical & Electronic
S. U. Rehman, M. Bilal, Mustafa Inc, U. Younas, H. Rezazadeh, M. Younis, S. M. Mirhosseini-Alizamini
Summary: The primary focus of this article is on cubic optical solitons in a polarization-preserving fiber modeled by the nonlinear Schrodinger equation. The authors secure a variety of optical soliton solutions, including hyperbolic and trigonometric solutions, as well as a class of solitary wave solutions. By using a new integration technique, the authors demonstrate that the obtained solutions are trustworthy and can be applied to more complex phenomena.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Physics, Multidisciplinary
Fiza Batool, Ali Raza, Sami Ullah Khan, Maimona Rafiq, M. Ijaz Khan
Summary: In this paper, exact solutions of the generalized coupled integrable dispersionless system (CIDS) are considered using the modified Kudryashov method and modified (G'G(2))-expansion method. Various kink wave solutions with adjustable parameters are obtained using the established techniques. The 3D graphic representation of the solutions with suitable parameters is presented. The techniques employed in this article are of great importance in calculating soliton solutions for nonlinear models in mathematical physics.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
J. Bonetti, D. F. Grosz, S. M. Hernandez
Summary: A new equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles is introduced in this study. By deriving a novel stochastic photon-conserving nonlinear Schrodinger equation suitable for modeling arbitrary nonlinear profiles, the study greatly enhances the understanding of fiber-based quantum devices and addresses issues of unphysical results.
PHYSICAL REVIEW LETTERS
(2021)
Article
Nanoscience & Nanotechnology
Weiguo Zhang, Yuli Guo, Siyu Hong, Xingqian Ling
Summary: This paper investigates the exact solitary wave solutions, periodic wave solutions, and bounded rational function solution of the high-order nonlinear Schrodinger equation, establishing a relationship between the solutions and the Hamilton energy of their amplitude. The study reveals that the evolutional relationships between solitary and periodic wave solutions are essentially determined by the energy change in the Hamilton system corresponding to their amplitude. Diagrams are provided to demonstrate the evolution from periodic wave solutions to solitary wave solutions as Hamilton energy changes.
Article
Multidisciplinary Sciences
Muhammad Shakeel, Salman A. Alqahtani, Muhammad Junaid U. Rehman, Grzegorz Kudra, Jan Awrejcewicz, Abdulaziz M. Alawwad, Abdullilah A. Alotaibi, Mejdl Safran
Summary: This paper analyzes the coupled nonlinear fractional Drinfel'd-Sokolov-Wilson (FDSW) model with beta derivative, which is important in describing dispersive water wave structures. The paper applies the travelling wave transformation and the generalized rational exponential function method to obtain various soliton solution structures and discuss the modulation instability for the model.
SCIENTIFIC REPORTS
(2023)
Article
Multidisciplinary Sciences
Di Zhou, D. Zeb Rocklin, Michael Leamy, Yugui Yao
Summary: The research establishes an analytic methodology to define the topological invariant of nonlinear normal modes and shows that strongly nonlinear topological boundary modes are guaranteed by nontrivial topological index.
NATURE COMMUNICATIONS
(2022)
Article
Physics, Applied
H. Blas, M. Cerna Maguina, L. F. dos Santos
Summary: Modifications of the nonlinear Schrödinger models show that MNLS models possess infinite towers of quasi-conservation laws for soliton configurations with a specific symmetry. Numerical simulations support the analytical results, demonstrating elastic scattering of bright solitons for a wide range of parameters. The potential applications of these results in various areas of nonlinear physics are discussed.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2021)
Article
Physics, Multidisciplinary
Dahirou Mahmoud, Saidou Abdoulkary, Alidou Mohamadou
Summary: We study the dynamics of modulated waves in a discrete coupled left-handed nonlinear transmission line using a two-dimensional nonlinear Schrodinger equation. By solving the boundary value problem and calculating the eigenvalues, we find that the system supports bright solitons in both transverse and longitudinal directions. The numerical simulations confirm the stability and propagation properties of the soliton.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Applied
Wen-Rong Sun, Meng-Meng Liu
Summary: In this study, we investigate the stability of elliptic solutions to the integrable defocusing fourth order nonlinear Schrodinger equation (4NLS) under subharmonic perturbations. By utilizing the squared-eigenfunction connection, we establish the spectral stability by linking the Lax spectrum to the stability spectrum. Furthermore, we demonstrate the orbital stability of elliptic solutions to the 4NLS equation by constructing a Lyapunov functional.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Physics, Fluids & Plasmas
Marco Nizama, Manuel O. Caceres
Summary: The attenuation of plane waves in conducting media and its relationship with global disorder were studied in this research. By solving the stochastic telegrapher's equation in the Fourier-Laplace representation, we determined the space penetration length of plane waves in complex conducting media. The critical value kc for Fourier's modes was found to determine wave localization. The inverse proportionality between the penetration length L = kc-1 and kc provides important information for characterizing wave propagation with Markovian and non-Markovian fluctuations in energy absorption rate. Additionally, intermittent fluctuations in energy absorption rate were also investigated.
Article
Optics
Yakup Yildirim
Summary: This paper successfully recovers various types of optical solitons by investigating the dynamics of soliton pulse propagation through optical fibers using the Biswas-Arshed equation.
Article
Mathematics, Applied
Telman A. Gadzhimuradov
Summary: The dynamics of envelope solitons in coupled anharmonic chains are studied. It is found that multi-component solitons can exhibit characteristics of free scalar solitons with arbitrary velocities and amplitudes. Exact multi-soliton solutions are provided and shown to be a linear interference of degenerate vector solitons. The interference idea is also applicable to other vector integrable systems, such as the Manakov model.
Article
Optics
Abdul-Majid Wazwaz
Summary: This study investigates an extended (2+1)-dimensional perturbed nonlinear Schrodinger equation with Kerr law nonlinearity in a nano optical fiber. The inclusion of fourth-order spatial derivatives allows for the study of nonlinearity and spatial dispersion effects in the x and y directions. Optical soliton solutions of various types, such as bright solitons and dark solitons, are extracted using useful soliton ansatzes, demonstrating the capability of identifying exact solutions for nonlinear evolution equations in different fields.
Article
Engineering, Multidisciplinary
Amin Gholami, Davood D. Ganji, Hadi Rezazadeh, Waleed Adel, Ahmet Bekir
Summary: The paper introduces a strong method called the modified Mickens iteration technique for solving a strongly nonlinear system, with applications in the field of nonlinear vibrations and oscillation systems. The method shows promising results in terms of accuracy and convenience, making it a potential candidate for solving other nonlinear problems in science and engineering.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Optics
Asim Zafar, M. Shakeel, Asif Ali, Hadi Rezazadeh, Ahmet Bekir
Summary: In this paper, optical solitons and other solutions of the Complex Ginzburg-Landau equation with the beta time derivative are analyzed in nonlinear optics. The kink, bright, and dark solitons of the model are obtained using the (m+(G '/G))-expansion method, and the precise solutions are graphically displayed. Some relatively novel solutions and conclusions are obtained from the analysis of the model, which serves as a reference for the development of the Ginzburg-Landau equation in nonlinear optics.
JOURNAL OF NONLINEAR OPTICAL PHYSICS & MATERIALS
(2023)
Article
Optics
Ali Zabihi, Mayssam Tarighi Shaayesteh, Hadi Rezazadeh, Reza Ansari, Nauman Raza, Ahmet Bekir
Summary: This paper investigates the soliton solutions of a higher-order dispersive cubic-quintic Schrodinger equation that describes the dynamics of ultrashort pulses in optical fibers. The multi-linear variable separation approach is used to derive a series of soliton solutions and plot dark and periodic wave solutions. The credibility of the results is verified by substituting each solution back into its governing equation. Different forms of wave solutions are depicted through portraits, and the constraints on the parameters for the existence of the obtained solutions are also provided.
JOURNAL OF NONLINEAR OPTICAL PHYSICS & MATERIALS
(2023)
Article
Optics
Emad H. M. Zahran, Ahmet Bekir
Summary: In this paper, new optical soliton solutions are generated using the extended direct algebraic method. These solutions have important applications in nonlinear fiber optics and photonic crystal fibers.
JOURNAL OF OPTICS-INDIA
(2023)
Article
Physics, Applied
Adem C. Cevikel, Ahmet Bekir, Ozkan Guner
Summary: The Fitzhugh-Nagumo equation is a significant nonlinear reaction-diffusion equation used for modeling nerve impulse transmission. Apart from its application in population genetics in biology, this equation is also widely utilized in circuit theory. In this study, we provided solutions to the fractional Fitzhugh-Nagumo (FN) equation, the fractional Newell-Whitehead-Segel (NWS) equation, and the fractional Zeldovich equation. Exact solutions within the framework of time fractional conformable derivative were obtained for these equations.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Maha S. M. Shehata, Ahmet Bekir
Summary: In this study, new perceptions of solitary wave solutions to the modified nonlinear Schrodinger equation are implemented. The achieved solutions describe new vision in terms of rogue wave modes, waves occurring only in positive cubic nonlinearity regime, waves occurring in the regime coinciding with the existence of instabilities of plane waves, and the long-wave limit of a breather. Two different schemas, the solitary wave ansatz method and the extended simple equation method, are employed to construct these new perceptions. A comparison is made between the obtained new perceptions and the old ones.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Engineering, Electrical & Electronic
Khalid K. Ali, Salman A. AlQahtani, M. S. Mehanna, Ahmet Bekir
Summary: In this study, three efficient methods, namely the Sardar sub-equation approach, the Bernoulli sub-ODE method, and the generic Kudryashov's method, are used to provide various families of solutions for the (2+1) Fokas system. Our suggested approaches offer several types of function solutions, including hyperbolic, trigonometric, power, exponential, and rational functions. Numerous graphs are presented at the end of the text to highlight the many solutions found.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
M. T. Darvishi, Mohammad Najafi, Somayeh Baloch Arbabi, Hadi Rezazadeh, Ahmet Bekir, Adem Cevikel
Summary: Searching for soliton solutions of nonlinear partial differential equations is an interesting and important area of research in the field of nonlinear phenomena. In this work, two extensions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation are studied, and new multiple front wave solutions are obtained using the simplified Hirota's method and the Cole-Hopf transformation method.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
Emad H. M. Zahran, Ahmet Bekir, Reda A. Ibrahim
Summary: In this article, the extended simple equation method (ESEM) and the extended direct algebraic method (EDAM) were used to extract the soliton solutions of the anti-cubic nonlinear Schrodinger equation, which is widely used in the field of optics. The rational solutions obtained through these methods highlight their importance. Additionally, the differential transform method (DTM) was implemented to construct corresponding numerical solutions for the achieved soliton solutions and compare them with the solutions obtained by ESEM and EDAM. The novelty of the achieved solutions is demonstrated in comparison with [1].
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
Emad H. M. Zahran, Ahmet Bekir
Summary: In this study, three different methods, namely the (G'/G)-expansion method, the extended simple equation method, and the Paul-Painleve approach method, were introduced to provide various novel analytical solutions to the nonlinear Schrodinger equation. The obtained results include various types of soliton solutions. The proposed model is important for describing wave propagation in optical fibers, which plays a fundamental role in telecommunications, medicine, and ocean engineering technologies. The uniqueness of the obtained results is demonstrated by comparing them with previous studies using different techniques.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
Emad H. M. Zahran, Ahmet Bekir
Summary: In this study, new optical soliton and rational soliton solutions are extracted using three different techniques. These solutions are crucial for understanding the dynamics of solitons in nonlinear optics.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
Ahmed M. Elsherbeny, Ahmet Bekir, Ahmed H. Arnous, Maasoomah Sadaf, Ghazala Akram
Summary: In this study, the dynamics of a perturbed fractional Radhakrishnan-Kundu-Lakshman (RKL) equation were investigated by considering fractional derivatives. A new simple equation method was used to construct precise wave solutions and the variation of soliton solutions with increasing fractional order of time derivative was observed. The results are significant for understanding the physical characteristics of soliton propagation in optical fiber.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Physics, Multidisciplinary
A. Bekir, E. H. M. Zahran
Summary: In this study, new configurations of the analytical solutions to the reaction-convection-diffusion equation (RCDE) have been achieved using the Paul-Painleve approach method (PPAM) and the (G'/G)-expansion method. These configurations have significant applications in mathematical physics and biological science. Furthermore, numerical solutions analogous to the analytical solutions have been obtained using the variational iteration method (VIM), which is known for providing accurate numerical solutions.
ROMANIAN JOURNAL OF PHYSICS
(2023)
Article
Mathematics, Applied
Emad H. M. Zahran, Omar Abu Arqub, Ahmet Bekir, Marwan Abukhaled
Summary: The main purpose of this study was to generate abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, which represents unstable optical solitons that result from optical propagations through birefringent fibers. These new soliton solutions exhibit bright, dark, W-shaped, M-shaped, periodic trigonometric, and hyperbolic behaviors that have not been observed before using any other method. Four different techniques, including the extended simple equation method, the Paul-Painleve approach method, the Ricatti-Bernoulli-sub ODE, and the solitary wave ansatz method, were used to detect these new solitons. These new solitons will contribute to future studies on both this model and optical propagations through birefringent fiber.
Article
Physics, Multidisciplinary
Muhammad Raheel, Asim Zafar, Muhammad Sarfraz Nawaz, Ahmet Bekir, Kalim U. Tariq
Summary: This study introduces new optical wave solutions for solving the time-fractional Kudryashov equation. These solutions offer a better representation of the nonlinear fractional model. The obtained solutions include dark, singular, singular-dark solitons, and others under certain conditions. Mathematica software is used to verify the obtained results. The modified integration method, the extended Jacobi's elliptic expansion functions method, is employed to obtain these solutions. These optical solitons demonstrate the effectiveness, simplicity, and reliability of this method compared to others.
PRAMANA-JOURNAL OF PHYSICS
(2023)
