Article
Optics
Abdul-Majid Wazwaz, S. A. Khuri
Summary: This work introduces two new sixth-order (3+1)-dimensional nonlinear Schrödinger equations with higher-order dispersive terms influenced by cubic-quintic-septic (CQS) nonlinearities. Bright and dark optical soliton solutions are formally retrieved for each model, along with certain constraints on parameters. Additionally, other solutions of distinct structures, such as singular solutions, are formally determined.
Article
Mathematics, Applied
Xue-Hui Zhao, Shuxia Li
Summary: This paper investigates a variable coefficient higher-order Schrodinger equation with the effects of third-order dispersion, self-steepening, and stimulated Raman scattering, which describes the propagation of ultrashort optical pulses in dispersion decreasing fibers. The bilinear forms, dark one-and two-soliton solutions are derived through symbolic computation and Hirota method. Graphical illustrations show the propagation and interaction of dark solitons, where the shape is influenced by the effects mentioned above and the amplitude and velocity are affected by the gain coefficient Gamma.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Optics
Abdul-Majid Wazwaz, Haifa A. Alyousef, Sherif M. E. Ismaeel, Samir A. El-Tantawy
Summary: This study derives different solutions for a (2+1)-dimensional nonlinear Schrodinger equation with fourth-order nonlinearity and dispersion, including bright and dark optical modulated solitons. Various conditions for the parameters are considered, resulting in bright, dark, periodic, exponential, and singular modulated solutions. These derived solutions can enhance the understanding of the features of bright and dark optical modulated solitons in optical fields, fluid mechanics, and plasmas.
Article
Optics
Wen-Hui Zhu, Jian-Guo Liu
Summary: In this study, a fifth-order nonlinear Schrodinger equation with variable coefficients is investigated to understand the diffusion of ultrashort pulses in incompatible optical fibers. Non-traveling wave bright and dark soliton solutions are obtained using two direct functions. Additionally, non-traveling wave hyperbolic-type and trigonometric-type solutions are studied using the G'/G-expansion method. Dynamic properties and characteristics of these derived results are demonstrated using three-dimensional figures and contour figures.
Article
Optics
Abdul-Majid Wazwaz, Weaam Alhejaili, S. A. El-Tantawy
Summary: This investigation explores both bright and dark envelope optical solitons in a (2+1)-dimensional cubic nonlinear Schrodinger equation. Different powerful ansatze are used to obtain exact analytical solutions for bright and dark solitons in the mentioned model, which is characterized by cubic nonlinearity. Additionally, other types of structures including singular, periodic, exponential solutions, and new forms of rational solutions are formally derived. This work demonstrates the significant contribution of cubic nonlinearity to optical solitons, recovering dark and bright soliton solutions as well as various other solutions in the model.
Article
Mathematics, Applied
Angel Paredes, Jose R. Salgueiro, Humberto Michinel
Summary: We investigate topologically charged propagation-invariant eigenstates of a 1+2-dimensional Schrodinger equation with a cubic-quintic nonlinear term. We derive a simple formula for the bright vortex ring's inner and outer radii and analyze dark soliton solutions, finding an eigenvalue cutoff dependent on the topological charge. Additionally, we study the azimuthal stability of the eigenstates and find they are stable for all propagation constants, at least for small topological charges.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Physics, Multidisciplinary
K. Hosseini, M. Mirzazadeh, D. Baleanu, N. Raza, C. Park, A. Ahmadian, S. Salahshour
Summary: In this study, 1-soliton solutions of the generalized complex Ginzburg-Landau model were obtained using exponential and Kudryashov methods, considering perturbation effects. The impact of parameter regimes on the dynamics of dark and bright soliton solutions in three- and two-dimensional postures was analyzed. The validity of all exact solutions presented in this study was successfully confirmed through the use of a symbolic computation system.
EUROPEAN PHYSICAL JOURNAL PLUS
(2021)
Article
Mathematics, Interdisciplinary Applications
Lu Tang
Summary: This paper studies the dynamical behavior and dispersive optical solitons in birefringent fibers with coupled Schrodinger-Hirota equation. By applying traveling wave transformations and the theory of planar dynamical system, a range of solutions with different waveforms are obtained. The single traveling wave solutions for the coupled nonlinear Schrodinger-Hirota equation are classified using the complete discriminant system method and symbolic computation, improving upon existing conditions and proposing a new method for constructing dispersive optical solitons.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Optics
Abdul-Majid Wazwaz, Mona Mehanna
Summary: This work introduces a generalized nonlinear Sasa-Satsuma equation with bright and dark optical soliton solutions, as well as other singular and exponential solutions of different structures.
Article
Optics
Lu Tang
Summary: The main purpose of this work is to study the dynamical behavior and optical soliton solutions for the stochastic nonlinear Schrodinger equation with multiplicative white noise and spatio-temporal dispersion. We analytically constructed periodic wave solutions, bell-shaped solitary wave solutions, and kink-shaped solitary wave solutions using the bifurcation theory of dynamical system. Additionally, with the help of the complete discriminant system method and symbolic computation, a range of new optical soliton solutions have been derived, including Jacobian elliptic function solutions, rational function solutions, and implicit analytical solutions. It is worth noting that the obtained optical solitons in this paper substantially improve the corresponding results in the known literature. Finally, we compared our solutions with those of others.
Article
Optics
Lu Tang
Summary: This paper studies the dynamical behaviors and optical solitons in DWDM networks with the Schrodinger-Hirota equation. New soliton solutions are obtained and various optical soliton solutions are constructed. These findings are significant for understanding and applying optical communication networks.
Article
Mathematics, Interdisciplinary Applications
Weitian Yu, Wenjun Liu, Hongxin Zhang
Summary: Via the Hirota method, the transmission of soliton molecules in different backgrounds and the effects of phase shift on them in the optical fiber system are illustrated. The elastic and inelastic collisions of dark and anti-dark solitons in various backgrounds are studied, and the controls of loss/gain coefficients on the backgrounds are revealed.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Computer Science, Interdisciplinary Applications
Zehra Pinar Izgi
Summary: The classical nonlinear Schrodinger equations with cubic and power nonlinearity have many applications in various fields such as nonlinear optics, plasma physics, superconductivity, and ocean waves. This paper proposes a generalized form of the modified nonlinear Schrodinger equation with various nonlinearities and obtains novel soliton solutions using the Bernoulli equation method. The results suggest potential improvements for the application of this model.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Materials Science, Multidisciplinary
Behzad Ghanbari, Dumitru Baleanu
Summary: Finding optical soliton solutions to nonlinear PDEs has become a popular topic. This study aims to identify diverse wave solutions to a generalized version of the nonlinear Schrodinger equation. Two modifications to the exponential rational function method are investigated. The results show that both techniques are efficient and easy to follow, and can determine wave solutions of various PDEs.
RESULTS IN PHYSICS
(2023)
Article
Optics
Abdul-Majid Wazwaz, Mona Mehanna
Summary: In this work, a new (3+1)-dimensional nonlinear Schrodinger equation influenced by cubic nonlinearity and spatial dissipations effects is studied. Bright and dark optical soliton solutions for this higher dimensional Schrodinger model are formally retrieved, along with other singular and periodic solutions of distinct structures.
Article
Physics, Multidisciplinary
S. A. El-Tantawy, Alvaro H. Salas, Ma'mon Abu Hammad, Shreif M. E. Ismaeel, D. M. Moustafa, E. El-Awady
Summary: This study numerically examines propagating nonlinear dissipative dust-acoustic breathers and rogue waves in electron-depleted dusty plasmas with two superthermal ions of different temperatures, considering the effects of dust viscosity and damping. The research presents a damped/modified nonlinear Schrodinger equation (DNLSE) to investigate the impact of dust kinetic viscosity on breather structures and rogue waves, providing insights into the excitation of dust-acoustic waves in Earth's magnetotail.
WAVES IN RANDOM AND COMPLEX MEDIA
(2021)
Article
Nanoscience & Nanotechnology
Ma'mon Abu Hammad, Alvaro H. Salas, S. A. El-Tantawy
Article
Multidisciplinary Sciences
Sawsan Abuhammad, Reem Hatamleh, Mohammad Alrawashdeh, Nasr Alrabadi, Tareq Mukattash, Mai Abuhammad, Kimberly Howard
Summary: This study evaluated the impact of personal attributes of Jordanian undergraduate health students on their attitudes toward substance use disorder (SUD) and identified age, gender, and previous experience as significant factors affecting attitude.
Article
Mathematics
Ma'mon Abu Hammad
Summary: In this paper, conformable Lebesgue measure and conformable fractional countable martingales are defined, and some convergence theorems are proved.
Article
Mathematics
Ma'mon Abu Hammad, Sh. AlSharif, R. Khalil, A. Shmasneh
Summary: In this article, a new definition of the fractional derivative is used to reformulate the second order Bessel differential equation. The solution of the fractional differential equation is obtained using power series. Additionally, the generating function is found and used to prove some standard results and recurrence relations. Finally, applications and integral representations of Bessel functions of fractional type, including sine and cosine, are presented.
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS
(2022)
Article
Mathematics
Mamon Abu Hammad, Hamza Alzaareer, Hassan Al-Zoubi, Hemen Dutta
JOURNAL OF INTERDISCIPLINARY MATHEMATICS
(2019)
Article
Mathematics
Roshdi Khalil, Mohammed Al Horani, Mamon Abu Hammad
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
(2019)
Proceedings Paper
Computer Science, Information Systems
Amer Dababneh, Bilal Albarmawi, Ma'mon Abu Hammad, Amjed Zraiqat, Tareq Hamadneh
2019 IEEE JORDAN INTERNATIONAL JOINT CONFERENCE ON ELECTRICAL ENGINEERING AND INFORMATION TECHNOLOGY (JEEIT)
(2019)
Proceedings Paper
Computer Science, Information Systems
Shatha Hasan, Asad Freihet, Ma'mon Abu Hammad, Mohammed Al-Smadi, Omar Abu Arqub, Shaher Momani
2019 IEEE JORDAN INTERNATIONAL JOINT CONFERENCE ON ELECTRICAL ENGINEERING AND INFORMATION TECHNOLOGY (JEEIT)
(2019)
