Article
Materials Science, Multidisciplinary
Anjan Biswas, Abdul H. Kara, Yunzhou Sun, Qin Zhou, Yakup Yildirim, Hashim M. Alshehri, Milivoj R. Belic
Summary: This paper discusses the conserved densities and quantities for the perturbed complex Ginzburg-Landau model using Lie symmetry analysis, and finds that for certain nonlinear forms, the Hamiltonian ceases to exist due to divergent integrals.
RESULTS IN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Hashim M. Alshehri, Anjan Biswas
Summary: This paper presents the conservation laws for optical solitons with cubic-quantic-septic-nonic nonlinearity. The adiabatic dynamics of the conserved quantities are obtained using soliton perturbation theory. The phenomenon of optical soliton cooling is finally revealed.
Article
Materials Science, Multidisciplinary
A. A. Altwaty, Saleh M. Hassan, Bader R. K. Masry
Summary: This paper presents dark optical solutions for generalized anti-cubic nonlinearity in fiber Bragg gratings, including fractional temporal evolution. The soliton solution appears with restriction conditions, using modified Riemann-Liouvill derivative and fractional Riccati method.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Anjan Biswas, Abdul H. Kara, Mehmet Ekici, Elsayed M. E. Zayed, Abdullah K. Alzahrani, Milivoj R. Belic
Summary: This paper implements a multiplier approach to exhibit conservation laws in magneto-optic waveguides that maintain anti-cubic as well as generalized anti-cubic forms of the nonlinear refractive index. Three conservation laws are retrieved for each form of nonlinearity, including power, linear momentum, and Hamiltonian. The conserved quantities are computed from their respective densities.
REGULAR & CHAOTIC DYNAMICS
(2021)
Article
Engineering, Electrical & Electronic
Harun Bolukbasi, Mehmet Ekici, Anjan Biswas
Summary: This paper uncovers a complete spectrum of soliton solutions from a governing model with anti-cubic law of nonlinear refractive index. It implements Jacobi's elliptic function scheme and a limiting approach for the corresponding modulus of ellipticity. The criteria for the existence of such solitons are also enumerated.
OPTICAL AND QUANTUM ELECTRONICS
(2021)
Article
Multidisciplinary Sciences
Ahmed H. Arnous, Anjan Biswas, Abdul H. Kara, Yakup Yildirim, Luminita Moraru, Simona Moldovanu, Puiu Lucian Georgescu, Abdulah A. Alghamdi
Summary: This study implements three elegant approaches to recover a complete spectrum of optical solitons to the Radhakrishnan-Kundu-Lakshmanan equation with dual-power law of nonlinear refractive index. The conservation laws are also recovered by the usage of multipliers approach. The parameter constraints for the existence of such solitons are also enumerated. The numerical simulations of the recovered soliton solutions are also presented.
Article
Nanoscience & Nanotechnology
Raghda A. M. Attia, Mostafa M. A. Khater, A. El-Sayed Ahmed, M. A. El-Shorbagy
Summary: The research article discusses analytical and semi-analytical solutions to the quadratic-cubic fractional nonlinear Schrodinger equation. By transforming the fractional formula into an integer-order model using a new fractional operator, theoretical and computational approaches can now be applied to fractional models, yielding a large number of novel analytical strategies. The solutions obtained are used to describe shifts in physical structures over time in the presence of quantum effects, like wave-particle duality, and the precision of all analytical results is tested using Mathematica software 12.
Article
Engineering, Electrical & Electronic
Abbagari Souleymanou, Alphonse Houwe, A. H. Kara, Hadi Rezazadeh, Lanre Akinyemi, Serge P. T. Mukam, Serge Y. Doka, Thomas B. Bouetou
Summary: In this paper, a nonlinear wave equation modeling optical solutions in a weakly nonlocal and parabolic competing nonlinear medium is studied. Exact traveling wave solutions in hyperbolic, rational, and trigonometric functions multiplied by exponential functions are determined using the extended form of the Kudryashov method. The modulation instability growth rate is analyzed, and the stability of dark and bell-shaped solitons is substantiated using the split-step Fourier method. The propagation of solitonic waves with stable shape, sometimes tilting from right to left, is demonstrated compared to previous studies.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Physics, Multidisciplinary
Ahmed H. Arnous, Anjan Biswas, Abdul H. Kara, Yakup Yildirim, Hashim M. Alshehri, Milivoj R. Belic
Summary: This study introduces a new approach to obtain highly dispersive bright and singular optical solitons in the absence of self-phase modulation. The derived bright soliton solution is used to compute conserved quantities from their densities obtained by the application of multipliers approach.
Article
Optics
Annamalai Muniyappan, Shanmugham Amirthani, Palanivel Chandrika, Anjan Biswas, Yakup Yildirim, Hashim M. Alshehri, Dalal A. A. Maturi, Dalal H. Al-Bogami
Summary: This research investigates the anti-cubic and generalized anti-cubic nonlinearity in optical fibers. Dark soliton structures are obtained through the Jacobi elliptic function method and Jacobi elliptic function expansion method. Furthermore, the physical significance and dynamical behaviors of the dark soliton solutions are established using the dispersion coefficient as a physical parameter.
Article
Optics
Ahmed H. Arnous, Anjan Biswas, Mehmet Ekici, Abdullah K. Alzahrani, Milivoj R. Belic
Summary: This paper investigates soliton solutions to Kudryashov's equation using an improved approach, presenting bright, dark, and singular optical soliton solutions. The conserved quantities are also demonstrated.
Article
Optics
Nikolai A. Kudryashov, Anjan Biswas, Abdul H. Kara, Yakup Yildirim
Summary: This paper recovers dark and bright cubic-quartic optical solitons using the cubic-quintic-septicnonic nonlinear Schrodinger's equation, and then identifies the conserved quantities associated with the bright soliton using Gauss' hypergeometric functions.
Article
Optics
Yakup Yildirim, Anjan Biswas, Abdul H. Kara, Padmaja Guggilla, Salam Khan, Abdullah Khamis Alzahrani, Milivoj R. Belic
Summary: The paper obtains soliton solutions for Kudryashov's law from quadrupled power law and dual form of nonlocal nonlinearity. A full spectrum of soliton solutions are derived and the conservation law is also exhibited to provide a complete picture to the model.
Article
Optics
Jose Vega-Guzman, Anjan Biswas, Abdul Hamid Kara, M. F. Mahmood, Mehmet Ekici, Hashim M. Alshehri, Milivoj R. Belic
Summary: This study retrieves cubic-quartic soliton solutions to the Lakshmanan-Porsezian-Daniel model using the method of undetermined coefficients, with a focus on both polarization-preserving fibers and birefringent fibers. Conservation laws for polarization-preserving fibers are also recovered and enumerated, along with the presented existence criteria for the displayed solitons.
JOURNAL OF NONLINEAR OPTICAL PHYSICS & MATERIALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Mourad Soltani, Houria Triki, Faisal Azzouzi, Yunzhou Sun, Anjan Biswas, Yakup Yildirim, Hashim M. Alshehri, Qin Zhou
Summary: This research analyzes the dynamics of intense light pulses in an optical medium with cubic-quintic nonlinearity and pure fourth-order dispersion. The study reveals various periodic wave solutions in the system. Notably, two types of quartic dark solitons with equal amplitudes and wave numbers but different widths are identified in the long-wave limit for the first time.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Houria Triki, Qin Zhou, Wenjun Liu, Anjan Biswas, Luminita Moraru, Yakup Yildirim, Hashim M. Alshehri, Milivoj R. Belic
Summary: This article addresses the propagation of ultrashort light pulses in a birefringent optical fiber with various dispersion effects. The dynamics of the pulses are described by the coupled Fokas-Lenells equations, which provide an accurate description of pulse evolution in the femtosecond range. The study reports the first analytical demonstration of chirped solitons in a birefringent fiber medium and discusses their formation and characteristics.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Stanko N. Nikolic, Sarah Alwashahi, Omar A. Ashour, Siu A. Chin, Najdan B. Aleksic, Milivoj R. Belic
Summary: In this paper, the multi-elliptic rogue wave clusters of the nonlinear Schrodinger equation are analyzed to understand the origin and appearance of optical rogue waves in this system. The Darboux transformation scheme is used to obtain these structures on uniform backgrounds. The main outcomes of this research are the new multi-rogue wave solutions of the NLSE and its extended family.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Milivoj R. Belic, Stanko N. Nikolic, Omar A. Ashour, Najdan B. Aleksic
Summary: This article discusses the strange nature, dynamic generation, ingrained instability, and potential applications of rogue waves in oceans and optics. It presents solutions to the standard cubic nonlinear Schrodinger equation, which models many propagation phenomena in nonlinear optics. The article proposes a method for suppressing the modulation instability of rogue waves and demonstrates how rogue waves can be used to produce stable recurrent images in nanolithography. It also highlights instances when rogue waves appear as numerical artifacts and how statistical analysis based on different numerical procedures can lead to misleading conclusions about the nature of rogue waves.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Liangwei Zeng, Milivoj R. Belic, Dumitru Mihalache, Jincheng Shi, Jiawei Li, Siqi Li, Xiaowei Lu, Yi Cai, Jingzhen Li
Summary: We have demonstrated the existence of various types of gap localized modes, including one- and two-dimensional solitons and soliton clusters, as well as vortex modes, in optical media with saturable Kerr nonlinearity and fractional diffraction. We found that soliton clusters with different peak numbers can be stable, and the localized modes at the center of the first and second band gaps are stable. The stability of these modes is confirmed through linear stability analysis and numerical simulations.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Omar A. Ashour, Siu A. Chin, Stanko N. Nikolic, Milivoj R. Belic
Summary: We investigated higher-order breathers of the cubic nonlinear Schrodinger equation on a periodic elliptic background. We found that, beyond first order, any arbitrarily constructed breather on a disordered background generates a single-peaked solitary wave. However, on the periodic backgrounds, the so-called quasi-rogue waves, which are quasiperiodic breathers with distorted side peaks, are more common. We constructed such higher-order breathers using constituent first-order breathers with commensurate periods and also found truly periodic breathers, but they are rare and require finely tuned parameters.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Liangwei Zeng, Xing Zhu, Milivoj R. Belic, Dumitru Mihalache, Jincheng Shi, Junbo Chen
Summary: In this study, it is proven that inhomogeneous defocusing cubic nonlinear media described by the nonlinear Schrodinger equation can support one-dimensional multiple-peak and two-dimensional multiple-ring solitons with equal intensity peaks. The number of equal peaks depends on the parameters describing nonlinearity. Furthermore, vortical modes in these media exhibit alternating stability and instability domains, unlike their non-vortical counterparts which are completely stable.
NONLINEAR DYNAMICS
(2023)
Article
Engineering, Mechanical
Liangwei Zeng, Jincheng Shi, Milivoj R. Belic, Dumitru Mihalache, Junbo Chen, Hu Long, Xiaowei Lu, Yi Cai, Jingzhen Li
Summary: It is demonstrated that both fundamental and multipole soliton families can be generated and stabilized in saturable nonlinear lattices, which have practical applications in nonlinear optics and Bose-Einstein condensates.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Qing Wang, Dumitru Mihalache, Milivoj R. Belic, Liangwei Zeng, J. Lin
Summary: This paper introduces a novel method for realizing soliton transformation between different potential wells by gradually manipulating their depths in the propagation direction. The method requires a smooth gradient of the manipulated depth and stable solitons in different potential wells. The comparison with iterative solitons proves the efficiency and reliability of the method, and it also shows that stable solitons can be obtained in complex potential wells where iterative numerical methods fail. The controllable soliton transformation provides opportunities for all-optical switching, optical information processing, and other applications.
Article
Computer Science, Information Systems
Ahmed H. Arnous, Anjan Biswas, Yakup Yildirim, Luminita Moraru, Simona Moldovanu, Seithuti P. Moshokoa
Summary: The study focuses on the application of the enhanced Kudryashov approach in dealing with the model of self-phase modulation, pointing out the limitations when the nonlinearity has a generalized form. In contrast to the common approach in the past, the current analysis employs a direct method rather than intermediate phase-portrait analysis.
Article
Optics
Liangwei Zeng, Milivoj R. Belic, Dumitru Mihalache, Dan Xiang, Qing Wang, Jianrong Yang, Xing Zhu
Summary: We demonstrate novel triangular bright solitons supported by the nonlinear Schrodinger equation with inhomogeneous Kerr-like nonlinearity and external harmonic potential, which can be realized in nonlinear optics and Bose-Einstein condensates. The profiles of these solitons differ from common Gaussian or sech envelope beams, with tops and bottoms resembling triangle and inverted triangle functions. Self-defocusing nonlinearity leads to triangle-up solitons, while self-focusing nonlinearity supports triangle-down solitons. The stability of these lowest-order fundamental triangular solitons is confirmed by linear stability analysis and direct numerical simulations.
Article
Physics, Multidisciplinary
Zhengping Yang, Wei-Ping Zhong, Milivoj R. Belic
Summary: We introduce ring-like toroidal breather solutions of the (2 + 1)-dimensional nonlinear Schrodinger equation with Kerr nonlinearity. By approximating the (2 + 1)-dimensional NLS equation in cylindrical coordinates with the standard (1 + 1)-dimensional NLS equation, we obtain the first-order toroidal breather solutions and investigate their dynamic characteristics. Notably, we discover and present the toroidal Peregrine soliton for the first time. This research can be extended to studying other high-dimensional nonlinear equations and provides a practical method for analyzing other high-dimensional nonlinear localized wave structures.
Article
Optics
Chengming Lyu, Milivoj R. Belic, Yongdong Li, Yiqi Zhang
Summary: In this paper, we investigate the generation and propagation of diffraction-free Bessel beams by combined axicons. Theoretical analysis and experimental results show that these beams can propagate up to 9.63 km in free space. By utilizing the angular spectrum reconstruction theory, the propagation distance can be extended up to 15 km. The self-healing property and outstanding performance of Bessel beams in weak to moderate turbulence atmosphere are also demonstrated.
OPTICS AND LASER TECHNOLOGY
(2023)
Article
Optics
Boquan Ren, Hongguang Wang, Milivoj R. Belic, Yongdong Li, Xiaoyu Zhu, Yiqi Zhang
Summary: Applying strain in photonic graphene can induce zero-energy edge states, which can be understood as a stack of Su-Schrieffer-Heeger chains.
Article
Materials Science, Multidisciplinary
Yakup Yidirim, Anjan Biswas, Hashim M. Alshehri, Milivoj R. Belic
Summary: This paper investigates cubic-quartic optical solitons for the perturbed Gerdjikov-Ivanov equation. Both the scalar case and birefringent fibers are considered. The perturbation terms are limited to the maximum permissible intensity. A complete spectrum of soliton solutions is recovered and listed.
OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS
(2022)
Article
Physics, Multidisciplinary
Qian Tang, Boquan Ren, Milivoj R. Belic, Yiqi Zhang, Yongdong Li
Summary: After more than 10 years of development, nonlinear topological photonics is emerging as a new branch of physics. One of the most interesting subjects in this field is the topological edge solitons, which are solitary structures that can move along the edges of photonic crystals with constant speed and maintain their profiles unchanged during long-distance propagation. This paper presents bright and dark valley Hall edge solitons in the kagome photonic lattice, which can circumvent sharp corners and have potential applications in the development of novel photonic chips.
ROMANIAN REPORTS IN PHYSICS
(2022)
