Article
Materials Science, Multidisciplinary
A. Safaei Bezgabadi, M. A. Bolorizadeh
Summary: This paper presents the analytic solutions of the generalized nonlinear Schrodinger equation (GNLSE) by implementing the extended SinhGordon equation expansion method (ShGEEM), which includes effects such as dispersion, waveguide's loss, Kerr Effect, self-steepening and Raman Effect. The obtained solutions represent bright, dark and combined bright-dark solitons, and constraint conditions for valid solutions are provided. New solutions are graphically shown for pulse propagation along a photonic crystal fiber.
RESULTS IN PHYSICS
(2021)
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
Mathematics, Applied
Xin Wang, Ling-Ling Zhang, John Fiifi Essel
Summary: In this paper, we investigate two classes of high-order nonlinear Schrodinger equations and obtain the concrete forms of soliton solutions by defining different ansatz equations. The method used is briefly summarized and explained, and applied to two specific classes of equations. Finally, the specific forms of solutions and the necessary conditions for their existence are obtained, with added pictures for better understanding.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Physics, Multidisciplinary
Yi-Xiang Chen
Summary: In this study, we focus on a nonlinear Schrodinger model and successfully construct two-component solutions with different structures using various transformations and techniques. By modifying parameters, we achieve control excitation of the solutions, resulting in different shapes.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Engineering, Mechanical
Li Chen, Haiping Zhu
Summary: This paper investigates the influence of different diffractions on the excitation of partially nonlocal vector rogue waves. By reducing the equation to a constant-coefficient vector nonlinear Schrodinger equation, analytical solutions are obtained. Using the nonrecursive Darboux method, partially nonlocal vector bright-dark rogue waves and bright-bright rogue wave pairs are revealed. The results deepen our understanding of ultrashort wave phenomena in various fields.
NONLINEAR DYNAMICS
(2023)
Article
Optics
H. Elzehri, A. H. Abdel Kader, M. S. Abdel Latif
Summary: In this paper, new soliton and doubly periodic solutions for the complex Ginzburg-Landau equation (CGLE) with two forms of nonlinearity are obtained using Lie symmetry method. The solutions are in the form of Jacobi and Weierstrass elliptic functions, and under certain conditions, kink wave, dark, and bright soliton solutions for the CGLE can be retrieved from the obtained doubly periodic solutions.
Article
Mathematics, Interdisciplinary Applications
Swapan Biswas, Uttam Ghosh, Santanu Raut
Summary: The present article focuses on the design and study of granular metamaterials, taking into consideration the impact of granular structures on wave propagation. By formulating the fractional granular equation, the propagating properties of wave quantities in rough granular media were investigated. Various complex solutions were explored using different analytical methods, demonstrating the crucial role of the order of derivative in the formation of different types of soliton solutions.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Optics
Yuqin Cui, Fenfen Ma
Summary: The main focus of this research is on finding solitary wave solutions for the variable coefficient nonlinear Schrodinger equation with an external potential, including bright soliton, dark soliton, periodic soliton, and triangular soliton derived through the complete discrimination system. Particularly, the Cross-shaped and T-shaped dark soliton are demonstrated.
Article
Engineering, Mechanical
Kamel Maddouri, Faical Azzouzi, Houria Triki, Abdesselam Bouguerra, Sabiha Amara Korba
Summary: The study focuses on the inhomogeneous higher-order nonlinear Schrodinger equation, investigating the dark soliton-type pulse propagation with cubic-quintic-septic nonlinear terms and gain or loss with variable coefficients. A novel dark-managed soliton structure with a sech(2/3) profile is found, different from traditional tanh dark solitons in Kerr-type media. The stability of these solitons under initial perturbations is also explored, along with numerical investigations on the interaction dynamics of two and three dark-managed solitons.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Multidisciplinary
Serbay Duran, Bayhan Karabulut
Summary: Trigonometric and hyperbolic type traveling wave solutions are produced by using the sub-equation analytical method considering the Kerr Law properties of the equation defining nematic liquid crystals. The resulting traveling wave solutions play an important role in energy transport and soliton molecules in liquid crystals. In addition, solitary wave behaviors for different values of constants in the produced traveling wave solutions are discussed.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Mechanical
Qin Zhou, Mingyao Xu, Yunzhou Sun, Yu Zhong, Mohammad Mirzazadeh
Summary: This article investigates the transmission characteristics of ultrashort optical pulses in fibers by analyzing the coupled nonlinear Schrodinger equations. The results provide a new idea for the transformation of dark soliton states.
NONLINEAR DYNAMICS
(2022)
Article
Materials Science, Multidisciplinary
Thilagarajah Mathanaranjan
Summary: In this study, a (2 + 1)-dimensional nonlinear Schrodinger equation with fractional-order derivative was considered and newly derived using the fractional variational principle and the semi-inverse method. By introducing the fractional complex transform, explicit analytical solutions were obtained using the (G'/G)-expansion method, the tanh-coth method, and the modified simple equation method, resulting in optical singular and dark soliton solutions. The behaviors of the soliton solutions were expressed by 2D and 3D graphs.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Sudipta Nandy, Abhijit Barthakur
Summary: The study investigates dark-bright soliton dynamics in a coupled nonlinear Schrodinger equation with complex potentials, examining interactions of soliton complexes under different potentials. It presents results of elastic and inelastic interactions between solitons under these potentials. The external potential causes notable changes in soliton dynamics by altering velocity, frequency, and wave number, with interesting features observed in complex three soliton interactions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Physics, Multidisciplinary
Nikolay A. Kudryashov
Summary: The generalized nonlinear Schrodinger equation for optical solitons in a saturable medium is studied using transformation variables to find solitary wave solutions. Analytical solutions for bright and dark solitons in a saturable medium are demonstrated.
Article
Physics, Mathematical
Renato Spigler
Summary: The quantum lattice Boltzmann (qlB) algorithm is used to approximate the 1D Dirac equations and the non-relativistic Schrodinger equation. This method provides accurate solutions in the non-relativistic limit, but with a small error.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Electrical & Electronic
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy
OPTICAL AND QUANTUM ELECTRONICS
(2018)
Article
Optics
Elsayed M. E. Zayed, Shoukry El-Ganaini, Abdul-Ghani Al-Nowehy, Mohamed E. M. Alngar
Editorial Material
Physics, Condensed Matter
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy
SUPERLATTICES AND MICROSTRUCTURES
(2018)
Editorial Material
Physics, Condensed Matter
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Mohamed E. M. Aingar, Reham M. A. Shohib
SUPERLATTICES AND MICROSTRUCTURES
(2018)
Article
Materials Science, Multidisciplinary
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Shoukry El-Ganaini, Reham M. A. Shohib
RESULTS IN PHYSICS
(2018)
Article
Mathematics, Applied
Elsayed M. E. Zayed, Reham M. A. Shohib, Abdul-Ghani Al-Nowehy
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2018)
Editorial Material
Optics
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Reham M. A. Shohib, Mohamed E. M. Alngar
Article
Optics
Elsayed M. E. Zayed, Mohamed E. M. Alngar, Abdul-Ghani Al-Nowehy
Article
Physics, Multidisciplinary
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Mona E. M. Elshater
EUROPEAN PHYSICAL JOURNAL PLUS
(2018)
Article
Engineering, Electrical & Electronic
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Reham M. A. Shohib
OPTICAL AND QUANTUM ELECTRONICS
(2019)
Article
Mathematics, Applied
Elsayed M. E. Zayed, Reham M. A. Shohib, Abdul-Ghani Al-Nowehy
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Physics, Multidisciplinary
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Mona E. M. Elshater
PRAMANA-JOURNAL OF PHYSICS
(2019)
Article
Optics
Elsayed M. E. Zayed, Taher A. Nofal, A. G. Al-Nowehy, Mohamed E. M. Alngar
Summary: Using new mapping approaches and extended auxiliary equation approaches, various solutions of the (2+1)-dimensional coupled nonlinear Schrodinger equations have been obtained, including solitons and other solutions. These solutions describe transverse effects in optical fibers, time-independent corporation, and the field of optical solitons.
Article
Engineering, Marine
Elsayed M. E. Zayed, Abdul-Ghani Al-Nowehy, Reham M. A. Shohib
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2019)
Article
Mathematics, Applied
Elsayed M. E. Zayed, A. -G Al-Nowehy, Mona E. M. Elshater
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS
(2018)