Article
Mathematics
Ahmed H. Arnous, Luminita Moraru
Summary: In this paper, optical soliton solutions for the complex Ginzburg-Landau equation with Kudryashov's law of refractive index are derived using an improved modified extended tanh-function technique. Bright and dark solitons, as well as singular soliton solutions, are obtained. Additionally, as the modulus of ellipticity approaches unity or zero, solutions are expressed in terms of Jacobi's elliptic functions, which yield solitons and periodic wave solutions.
Article
Mathematics, Interdisciplinary Applications
Orazio Descalzi, Carlos Cartes
Summary: This article investigates the formation of localized spatiotemporal chaos in the complex cubic Ginzburg-Landau equation with nonlinear gradient terms and reviews the influence of multiplicative noise on stationary pulses stabilized by nonlinear gradients. Surprising results are obtained through numerical simulations and explained analytically, including the induction of velocity change in propagating dissipative solitons.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ahmed H. Arnous, Anjan Biswas, Yakup Yildirim, Qin Zhou, Wenjun Liu, Ali S. Alshomrani, Hashim M. Alshehri
Summary: This paper implements the enhanced Kudryashov's method to address the solitons of the cubic-quartic complex Ginzburg-Landau equation. Different forms of self-phase modulation structures are studied, and the existence criteria for bright and singular solitons are indicated.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Ahmed H. Arnous, Taher A. Nofal, Anjan Biswas, Yakup Yildirim, Asim Asiri
Summary: This paper presents a method for extracting cubic-quartic optical soliton solutions for the complex Ginzburg-Landau equation with five distinct forms of nonlinear refractive index. By utilizing the proposed algorithm, a diverse range of optical solitons, including hybrid types, that satisfy the specified parameter restrictions can be obtained.
NONLINEAR DYNAMICS
(2023)
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
Optics
Valery E. Lobanov, Aleksey A. Kalinovich, Olga V. Borovkova, Boris A. Malomed
Summary: This article investigates the existence of stable two-dimensional dissipative solitons in optical media with quadratic nonlinearity. The authors introduce a localized amplifying region to compensate for loss in the system. The results demonstrate the stable solitons and vortex solitons that can be supported by implementing the appropriate gain distribution.
Article
Materials Science, Multidisciplinary
Shafiq Ahmad, Emad E. Mahmoud, Sayed Saifullah, Aman Ullah, Shabir Ahmad, Ali Akgul, Sayed M. El Din
Summary: This article investigates the significance of the unsteady nonlinear Landau-Ginzburg-Higgs equation in the context of superfluids and Bose-Einstein condensates. Through the utilization of the Sardar-subequation and energy balance approaches, a variety of new exact solutions are obtained, including different types of solitons. The findings contribute to the understanding of the equation and its application, surpassing previous efforts in the literature.
RESULTS IN PHYSICS
(2023)
Article
Engineering, Electrical & Electronic
Mario Zitelli, Mario Ferraro, Fabio Mangini, Stefan Wabnitz
Summary: A new semi-analytical model is proposed to describe the evolution of pulse bandwidth in dispersion managed transmission systems using multimodal and monomodal graded-index fibers. The model is compared with direct integration of the nonlinear Schrodinger equation and experimental results, showing the detrimental effects of dispersion and self-phase modulation interaction at high pulse powers. Promising results are found for spatio-temporal DM solitons in parabolic GRIN fibers.
JOURNAL OF LIGHTWAVE TECHNOLOGY
(2021)
Article
Optics
Neveen G. A. Farag, Ahmed H. Eltanboly, M. S. El-Azab, S. S. A. Obayya
Summary: In this study, the split-step Fourier transform (SSFT) method is used to analyze the complex Ginzburg-Landau (CGL) equation. Various types of optical soliton solutions are obtained using the numerical approach, and the results are found to be in agreement with the analytical solutions. This numerical technique can be applied to solve other nonlinear evolution partial differential equations in the field of mathematical physics.
Article
Optics
Elsayed M. E. Zayed, Taher A. Nofal, Mohamed E. M. Alngar, Mahmoud M. El-Horbaty
Summary: This research focuses on studying soliton solutions of perturbed CQ NLCGL equation with different nonlinear laws, and the integration scheme has made it possible to construct analytical solutions for combo-bright-singular, bright, dark, and singular optical solitons.
Article
Engineering, Multidisciplinary
Munyaradzi Rudziva, Precious Sibanda, Osman A. Noreldin, Sicelo P. Goqo
Summary: In this study, the influence of time-dependent rotational modulation on stability, heat, and mass transfer in a Darcy porous medium with a couple stress fluid is investigated theoretically. The effects of modulating rotation, solute gradient, and permeability on the stability of the porous medium are studied using a perturbation technique. The Ginzburg Landau equation is obtained and heat and mass transport are quantified using the Nusselt and Sherwood numbers respectively. The results show that increasing the modulation amplitude accelerates the heat and mass transport.
APPLIED MATHEMATICAL MODELLING
(2022)
Article
Optics
Elsayed M. E. Zayed, Mohamed E. M. Alngar, Reham M. A. Shohib, Taher A. Nofal, Khaled A. Gepreel
Summary: This article deduces soliton solutions for highly dispersive perturbed complex-Ginzburg-Landau equation in birefringent fibers with polynomial law of nonlinearity using two methods, the (G'/G)-expansion method and the addendum Kudryashov's method. The results include various types of soliton solutions and rational solutions.
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
Materials Science, Multidisciplinary
Sonia Akram, Jamshad Ahmad, Shafqat-Ur-Rehman, Shalan Alkarni, Nehad Ali Shah
Summary: This paper examines the fractional complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics and obtains exact solutions using the Hirota bilinear method. The instability modulation and gain spectra of the CGLE are also investigated. The results obtained are highly original and significant for describing phenomena in nonlinear optics and plasma physics.
RESULTS IN PHYSICS
(2023)
Article
Astronomy & Astrophysics
Chuan-Yin Xia, Hua-Bi Zeng, Yu Tian, Chiang-Mei Chen, Jan Zaanen
Summary: The AdS/CFT correspondence provides a unique method to study vortex matter phases in superconductors. By solving the dynamical evolution of a 2+1-dimensional superconductor at finite temperature and subjected to a magnetic field quench in terms of a gravitational hairy black hole in an asymptotic AdS 4 space, we can determine the nature of equilibrium states after the quench. Our results show the existence of Meissner phase and Abrikosov lattices under different external magnetic field conditions, consistent with the expectations of Ginzburg-Landau theory.
