Article
Mathematics, Interdisciplinary Applications
Xing Zhu, Shangwen Liao, Zhen Cai, Yunli Qiu, Yingji He
Summary: The study demonstrates the existence and stability of continuous soliton families in Kerr media with two-dimensional non-parity-time symmetric complex potentials. Discrete eigenvalues in the linear spectra of these complex potentials are observed, with fundamental solitons bifurcating from the largest discrete eigenvalue and dipole solitons from the second or third largest. Eigenvalues in the soliton linear-stability spectra are found to emerge as complex conjugate pairs, with the impact of different parameters on soliton stability discussed in detail. Additionally, transverse energy flow vectors of the solitons in these complex potentials are investigated.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Optics
J. B. Sudharsan, V. K. Chandrasekar, K. Manikandan, D. Aravinthan, G. Saadhana
Summary: This paper investigates the stable propagation of solitons in the presence of a PT-symmetric Gaussian potential in the CGL equation with self-focusing nonlinear mode. It emphasizes the manipulation of soliton dynamics by varying the strength of the imaginary part of the complex potential.
Article
Engineering, Mechanical
Niladri Ghosh, Amiya Das, Debraj Nath
Summary: This paper investigates the exact solutions and spectrum of the nonlinear Schrodinger equation with complex deformed supersymmetric potential. The study focuses on bright soliton and dark soliton solutions and their stability, which are validated by linear stability analysis and numerical simulations. Furthermore, the paper explores the stable regions of bright and dark solitons through adiabatic transformations of system parameters.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Wanwei Che, Feiwen Yang, Shulei Cao, Zhongli Wu, Xing Zhu, Yingji He
Summary: This study focuses on the existence and stability properties of gray solitons in parity-time (PT)-symmetric localized potentials with fractional-order diffraction. It is found that the Levy index and the real and imaginary parts of the complex potentials have significant influences on the solitons. Changing coefficients of PT-symmetric potentials in the nonlinear fractional Schrodinger equation can lead to a transition between gray solitons and anti-dark solitons. Additionally, the transverse energy flow in gray and anti-dark solitons with fractional-order diffraction is also discussed.
Article
Mathematics, Applied
Zijian Zhou, Jin Song, Weifang Weng, Zhenya Yan
Summary: This paper examines the properties of two types of PT-symmetric non-periodic potentials in the logarithmic nonlinear Schrodinger equation, including the existence, stability, and interaction of solitons, as well as the impact of time-dependent functions on solitons.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Yong Chen, Zhenya Yan, Boris A. Malomed
Summary: We studied a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials that can support exact solitons in one- and multi-dimensional nonlinear Schrodinger equation. In the 1D and multi-D settings, we found that a properly adjusted localization parameter may support fully real energy spectra. Continuous families of fundamental and higher-order solitons were produced. While the fundamental states were stable, the higher-order ones were unstable. The stable solitons were capable of robust propagation and remained trapped in slowly moving potential wells, which offers possibilities for manipulating optical solitons. Adiabatic variation of potential parameters could transform solitons into stable forms.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Physics, Multidisciplinary
Qi-Hao Cao, Chao-Qing Dai
Summary: The study focuses on the fractional second- and third-order nonlinear Schrodinger equation, deriving symmetric and antisymmetric soliton solutions and analyzing the influence of the Levy index on different solitons. Stability and stability intervals of solitons are discussed, with emphasis on the robustness of stable solitons against small disturbance.
CHINESE PHYSICS LETTERS
(2021)
Article
Engineering, Mechanical
Xing Zhu, Zhen Cai, Jinglin Liu, Shangwen Liao, Yingji He
Summary: This work demonstrates that non-parity-time-symmetric complex potentials can support continuous soliton families in competing cubic-quintic nonlinearities. The quintic nonlinearity coefficient influences the soliton existence and stability areas significantly.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Applied
Ming Zhong, Li Wang, Pengfei Li, Zhenya Yan
Summary: We report a novel spontaneous symmetry breaking phenomenon and the existence of ghost states in the framework of the fractional nonlinear Schrodinger equation. The symmetry of fundamental solitons is broken into two branches of asymmetry solitons (ghost states) with complex conjugate propagation constants, exclusively in fractional media. The influences of fractional Levy index (alpha) and saturable nonlinear parameters (S) on the symmetry breaking of solitons are analyzed in detail. Stability analysis, direct propagations, and collision phenomena between symmetric and asymmetric solitons are explored. The results provide a theoretical basis for studying spontaneous symmetry breaking phenomena and related physical experiments in fractional media with PT-symmetric potentials.
Article
Physics, Fluids & Plasmas
L. Al Sakkaf, U. Al Khawaja
Summary: The spectrum of bound states for modified Poschl-Teller and square-potential wells in the nonlinear Schrodinger equation is obtained. It is found that for a fixed norm, both potentials have a spectrum consisting of a finite number of multinode localized states. The existence of these localized states, which form as trapped modes, is confirmed through soliton scattering by the two potentials. The critical speed for quantum reflection is calculated using the energies of the trapped modes.
Article
Materials Science, Multidisciplinary
Sunam Jeon, Youngkuk Kim
Summary: The researchers propose a two-dimensional topological insulator, called 2DSWI, which is protected by inversion and time-reversal symmetries using two-dimensional SSH chains. The topological phase diagrams and phase transitions of 2DSWI are studied using the ZPA model, and it is found that the phase transition results in the formation of one-dimensional domain wall states. First-principles calculations predict that 2DSWI can be realized in 11 known materials.
Article
Mathematics, Applied
A. R. Thasneem, P. A. Subha
Summary: In this study, the stationary solutions of the coupled nonlinear Schrodinger equation with self-defocusing nonlinearity and super-Gaussian form of parity-time (PT) symmetric potential in an optical system are analyzed. The stationary eigenmodes of the ground and excited states and the influence of the gain/loss coefficient on the eigenvalue spectra are discussed. The threshold condition of the PT-symmetric phase transition of the high and low-frequency modes is studied, and the variation of the threshold values with the coupling constant and the effect of the nonlinearity on the eigenmodes are analyzed. The stability of the solution is verified using linear-stability analysis, and the power distribution of the fundamental solutions with the propagation in the PT and broken PT regimes in the two channels of the system is analyzed.
Article
Multidisciplinary Sciences
Tiecheng Wang, Xiang Gou
Summary: We investigated the band structures and scattering properties of a one-dimensional parity-time symmetric photonic crystal and discovered several interesting phenomena.
SCIENTIFIC REPORTS
(2022)
Article
Physics, Fluids & Plasmas
Zeyun Shi, Guoxiang Huang
Summary: We study the nonlinear dynamics of (2+1)-dimensional matter waves in a disk-shaped dipolar Bose-Einstein condensate with Lee-Huang-Yang correction. We find that the system supports (2+1)D matter-wave dromions and their stability is enhanced by the LHY correction. These dromions display interesting behaviors of collision, reflection, and transmission when interacting with each other and obstacles. This study contributes to the understanding of quantum fluctuations in BECs and the discovery of new nonlinear excitations.
Article
Astronomy & Astrophysics
Vladimir Dzhunushaliev, Vladimir Folomeev
Summary: In the non-Abelian SU(2) Proca-Higgs theory, localized axially symmetric solutions with finite field energy are studied. These solutions are shown to be analogs of the NielsenOlesen tube, but with some differences. The dependence of the total field mass of the Proca tube on one of the parameters determining the solution is examined in detail.
Article
Mathematics, Applied
U. Al Khawaja, S. M. Al-Marzoug, H. Bahlouli, F. Kh. Abdullaev
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2016)
Article
Optics
B. B. Baizakov, S. M. Al-Marzoug, U. Al Khawaja, H. Bahlouli
JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS
(2019)
Article
Optics
B. B. Baizakov, A. Bouketir, S. M. Al-Marzoug, H. Bahlouli
Article
Physics, Multidisciplinary
M. O. D. Alotaibi, B. B. Baizakov, S. M. Al-Marzoug, H. Bahlouli
Article
Physics, Multidisciplinary
U. Al Khawaja, S. M. Al-Marzoug, H. Bahlouli
Article
Optics
S. M. Al-Marzoug
Summary: This article investigates the parametric resonances of two coupled solitons in nonlocal nonlinear media in the presence of periodically varying intercomponent coupling coefficients, both analytically and numerically. The coupled equations of motion for the width and the center-of-mass coordinates of the solitons are derived and the resonant oscillations are analyzed numerically. The splitting condition and the theoretical predictions are confirmed by numerical simulations.
APPLIED PHYSICS B-LASERS AND OPTICS
(2022)
Article
Mathematics, Applied
Amaria Javed, T. Uthayakumar, M. O. D. Alotaibi, S. M. Al-Marzoug, H. Bahlouli, U. Al Khawaja
Summary: The dynamics of two component bright-bright (BB) solitons passing through different potentials were investigated to achieve unidirectional flow and segregation. A novel phenomenon called Polarity Reversal was observed, and the consistency between analytical and numerical analysis was confirmed through variational calculations.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
Article
Physics, Multidisciplinary
S. M. Al-Marzoug
Summary: By using a time-dependent variational approach, this study investigates the modulational instability of plane waves in Kerr media with nonlocal nonlinearity. Ordinary differential equations describing the evolution of modulational perturbations are obtained and analyzed, along with numerical simulations to confirm theoretical results. The level of nonlocality significantly impacts the behavior of modulational instability in the nonlinear stage.
Article
Optics
S. M. Al-Marzoug
Summary: The scattering of solitons by an asymmetric potential was investigated using a collective coordinate approach and numerical simulation. The center of mass and width of the soliton were analyzed. A detailed comparison between theoretical predictions and numerical simulations of a nonlinear Schrodinger equation is presented. The unidirectional flow of soliton was also studied numerically.
JOURNAL OF MODERN OPTICS
(2022)
Article
Physics, Multidisciplinary
Abdulaziz D. Alhaidari, Hocine Bahlouli, S. M. Al-Marzoug, Carlos P. Aparicio
Summary: This paper is a continuation of the previous study and presents a reformulation of the J-matrix theory through regularization of the inverse square singular potential. The objective is to restore rapid convergence in calculations and recover the conventional tridiagonal representation. Partial success has been achieved.
Article
Physics, Multidisciplinary
Abdulaziz D. Alhaidari, Hocine Bahlouli, Carlos P. Aparicio, S. M. Al-Marzoug
Summary: The J-matrix scattering method is developed for regular short-range potentials in atomic, nuclear, and molecular physics, showing advantages in accuracy and stability compared to other scattering methods. Recently extended to handle r-2 singular short-range potentials in sub-critical and supercritical coupling regimes, but with the cost of more complex algorithms and slower convergence.
Article
Optics
S. M. Al-Marzoug
Summary: This study investigates normal mode oscillations of anharmonically confined, one-dimensional, nonlocal nonlinear kerr media with repulsive long-range interaction. Both analytical and numerical methods are used, and the results show that frequency shifts caused by quartic distortion of the exciting potential are amplified by the long-range repulsive interaction. The study also reveals the presence of beating structure and higher harmonic modes.
Article
Physics, Fluids & Plasmas
M. O. D. Alotaibi, S. M. Al-Marzoug, H. Bahlouli, U. Al Khawaja
Article
Optics
U. Al Khawaja, P. S. Vinayagam, S. M. Al-Marzoug
Article
Mathematics, Applied
U. Al Khawaja, S. M. Al-Marzoug, H. Bahlouli
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2017)
