Article
Mathematics, Interdisciplinary Applications
Xiuye Liu, Jianhua Zeng
Summary: Dark solitons, localized nonlinear waves, have attracted significant attention due to their rich formation and dynamics in various fields. In this study, a purely nonlinear strategy is used to stabilize dark soliton stripes by introducing a quasi-one-dimensional Gaussian-like trap and combining it with an external linear harmonic trap. The results demonstrate complete stabilization of dark soliton stripes and a significant reduction in modulational instability.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Optics
Abdul-Majid Wazwaz
Summary: This study addresses soliton propagation in a sixth-order nonlinear Schrodinger equation with fourth-order and sixth-order dispersive terms influenced by cubic-quintic-septic nonlinearities. Bright and dark optical soliton solutions are formally derived, with constraints on parameters for determining these solutions. Other ansatze are employed to determine additional singular and periodic solutions. The findings could enhance understanding of wave dynamics in cubic-quintic-septic nonlinear materials such as chalcogenide glass.
Article
Mathematics, Interdisciplinary Applications
S. R. Li, Y. Y. Bao, Y. H. Liu, T. F. Xu
Summary: This paper studies the characteristics and stability of bright solitons in a fractional coupler with spatially periodical modulated nonlinearity. The results show that the amplitude, width, and stability of solitons are significantly influenced by the linear coupling constant, Levy index, chemical potential, and nonlinear intensity. The stability of bright solitons tends to increase with the increase of these parameters, and the distance between adjacent peaks in dipole and tripole solitons follows a specific multiple relation.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics
Tarek Saanouni
Summary: This note examines the asymptotic behavior of global solutions to the fourth-order Schrodinger equation for both local and non-local source terms, with scattering obtained in the defocusing mass super-critical and energy sub-critical regimes with radial setting.
POTENTIAL ANALYSIS
(2022)
Article
Mathematics, Applied
Munirah Alotaibi, Mohamed Jleli, Bessem Samet, Calogero Vetro
Summary: This study investigates the large-time behavior of solutions for the inhomogeneous nonlinear Schrodinger equation with different parameters, considering both the existence and nonexistence of global weak solutions. Critical exponents are calculated to reveal the impact of the nonlinearity on the Fujita critical exponent.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Optics
Vladimir Kruglov, Houria Triki
Summary: This study demonstrates the formation of periodic waves and envelope solitons in dispersive optical media with Kerr nonlinearity, under the influence of third-order dispersion and self-steepening effect. The stability of soliton solutions is proved using a stability criterion based on the theory of nonlinear dispersive waves. Modulation instability of continuous wave signals in dispersive optical media is also investigated, with results showing the dependency of the gain spectrum on the self-steepening parameter. Furthermore, a similarity transformation is presented to simplify the generalized extended nonlinear Schrodinger equation, and the propagation behaviors of self-similar solitons in different fiber systems are discussed.
Article
Mathematics, Applied
Li Wang, Zhenya Yan
Summary: This paper investigates novel nonlinear wave structures in the defocusing nonlinear Schrodinger equation, including stable new rogue waves (RW) and W-shaped solitons, as well as the interactions of RWs and the presence of RWs and W-shaped solitons in the case of complex PT-symmetric potentials.
APPLIED MATHEMATICS LETTERS
(2021)
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
Optics
Hatou-Yvelin Donkeng, Fabien Kenmogne, Chancelor Pokam Nguewawe, David Yemele
Summary: A coupled nonlocal nonlinear Schrodinger equation describing the propagation of polarized vector light pulses in a weakly anisotropic waveguide is introduced. The equation can support various polarization modes and the interaction between them can be controlled by adjusting parameters.
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS
(2021)
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
Mathematics, Applied
Ying Wang, Chengbin Xu
Summary: In this paper, the critical norm problem for the defocusing inhomogeneous nonlinear Schrodinger equations (INLS) is studied. By utilizing the concentration-compactness/rigidity method, it is shown that if a solution is uniformly bounded in the critical space throughout its lifespan, then the solution must be global and scatter.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
J. Bonetti, D. F. Grosz, S. M. Hernandez
Summary: A new equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles is introduced in this study. By deriving a novel stochastic photon-conserving nonlinear Schrodinger equation suitable for modeling arbitrary nonlinear profiles, the study greatly enhances the understanding of fiber-based quantum devices and addresses issues of unphysical results.
PHYSICAL REVIEW LETTERS
(2021)
Article
Mathematics, Applied
Liyuan Ma, Miaoshuang Fang, Haifang Song, Jiali Zhou
Summary: In this paper, the spatial property of the non-integrable discrete defocusing Hirota equation is investigated using a planar nonlinear discrete dynamical map method. Periodic orbit solutions of the stationary discrete defocusing Hirota equation are constructed, and the behavior of the orbits near the special periodic solution is analyzed. The effects of parameters on aperiodic orbits are characterized through numerical simulations. Moreover, it is found that the non-integrable discrete defocusing Hirota equation exhibits more abundant spatial properties compared to the non-integrable discrete defocusing nonlinear Schrodinger equation.
Article
Optics
Abdul-Majid Wazwaz
Summary: This study investigates an extended (2+1)-dimensional perturbed nonlinear Schrodinger equation with Kerr law nonlinearity in a nano optical fiber. The inclusion of fourth-order spatial derivatives allows for the study of nonlinearity and spatial dispersion effects in the x and y directions. Optical soliton solutions of various types, such as bright solitons and dark solitons, are extracted using useful soliton ansatzes, demonstrating the capability of identifying exact solutions for nonlinear evolution equations in different fields.
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
Engineering, Mechanical
Mateus C. P. dos Santos, Wesley B. Cardoso
Summary: The paper analyzes the spontaneous symmetry breaking induced by a specific component in a linearly coupled binary Bose-Einstein condensate. Through numerical simulations, symmetric and asymmetric ground states are obtained, and induced asymmetry in the partner field is observed, demonstrating the influence of linear coupling on the balance between atomic species and the appearance of Josephson and SSB phases.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
A. J. Balseyro Sebastian, D. Bazeia, M. A. Marques
Summary: We investigate the possibility of building internal structure and asymmetry for kinks and domain walls in scalar field theories in the multifield scenario. This requires including an extra field associated with a function that modifies the dynamics of the other fields. We study minimum energy configurations that support first order equations compatible with the equations of motion. The extra field allows for a transition guided by a parameter, connecting the standard solution to a geometrically constrained one, mimicking the effects of geometrical constrictions in magnetic materials.
Article
Engineering, Mechanical
Maurilho R. da Rocha, Ardiley T. Avelar, Wesley B. Cardoso
Summary: In this paper, we investigate a nonhomogeneous saturable nonlinear system described by a nonautonomous nonlinear Schrodinger equation and obtain localized solutions. By employing the similarity transformation technique, we convert the nonautonomous equation into an autonomous one. We further explore different modulation patterns that affect the position and width of the localized solutions and examine their linear stability.
NONLINEAR DYNAMICS
(2023)
Article
Optics
Xiuye Liu, Jianhua Zeng
Summary: This study theoretically investigates the phenomenon of nonlinear wave localizations in PT symmetric moire optical lattices. Different types of localized gap modes and their stabilization mechanisms are explored, including fundamental and higher-order gap solitons as well as vortical ones with topological charge. The stability regions of localized gap modes are examined through linear-stability analysis and direct perturbance simulations. This research provides an insightful understanding of soliton physics in combined versatile platforms of PT symmetric systems and moire patterns.
PHOTONICS RESEARCH
(2023)
Article
Physics, Multidisciplinary
Shu Zhou, Jianhua Zeng, Yali Qin
Summary: We investigate the existence and stability of localized gap states at a non-linear interface of non-linear fractional systems in a one-dimensional photonic lattice. We obtain the stability of the asymmetric localized gap states in the first and second finite gaps through direct numerical simulations and linear stability analysis. Our theoretical results provide insights into soliton physics in non-linear periodic systems with fractional-order diffraction, showing that the power of the localized gap states decrease gradually with the increase of propagation constant and the non-linear landscape.
FRONTIERS IN PHYSICS
(2023)
Article
Physics, Multidisciplinary
Mateus C. P. dos Santos, Wesley B. Cardoso
Summary: In this paper, a degenerate Fermi gas strongly confined in the transverse direction by a singular potential is studied. A one-dimensional effective equation is derived from a three-dimensional mean-field model using a variational approximation, which accurately describes the behavior of the particle distribution in the longitudinal direction. Systematic simulations confirm the reliability of the effective equation in describing the axial behavior of the tube-shaped Fermi gas in both attractive and repulsive regimes. Additionally, the 1D effective equation is found to be the best approximation for describing the periodic oscillations of the wave function in a dynamically changing potential.
Article
Astronomy & Astrophysics
D. Bazeia, A. S. Lobao Jr, M. A. Marques, R. Menezes
Summary: We investigate braneworlds modeled by topological solutions that arise from the Cuscuta-Galileon model. We develop a first order framework and illustrate our procedure using the hyperbolic tangent profile of the scalar field. We find conditions for the model parameters to have solutions connecting minima of the potential and interpolating Minkowski and anti de Sitter geometries, as well as solutions only interpolating anti de Sitter geometry. In both cases, the gravity sector of the brane is stable against metric fluctuations.
Article
Mathematics, Interdisciplinary Applications
I. Andrade, D. Bazeia, M. A. Marques, R. Menezes
Summary: In this study, we investigate a Maxwell-scalar model that couples the scalar field and gauge field either through electric permittivity or in the presence of impurity. By considering one-dimensional space, we identify the conditions under which the model with impurity can be treated as an effective model for the Maxwell-scalar system, yielding similar solutions. We also explore a specific class of impurities that modifies the core of the scalar field and find the corresponding nontrivial charge densities and electric fields.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Xiuye Liu, Jianhua Zeng
Summary: This article introduces the nonlinear localization of dense Bose-Einstein condensates (BECs) in a novel two-dimensional twisted periodic potential called Moire optical lattices, which bridge the gap between perfect optical lattices and aperiodic ones. The Moire optical lattices display wider second gaps and flat-band features, and support localized matter-wave structures like gap solitons and topological states within the finite gaps of the linear Bloch-wave spectrum. These localized structures have wide stability regions and can be readily implemented with currently available optical-lattice techniques.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Zhiming Chen, Zexing Wu, Jianhua Zeng
Summary: The search for three-dimensional spatiotemporal solitons has become a hot topic in nonlinear physics. This study investigates the formation and stability properties of light gap bullets in periodic media with defocusing nonlinearity. The results show that these light gap bullets, which exist within finite band gaps, can be stable under certain conditions.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Astronomy & Astrophysics
D. Bazeia, M. A. Liao, M. A. Marques
Summary: We investigate the presence of localized structures for relativistic scalar fields coupled to impurities in arbitrary spatial dimensions. It is shown that the inclusion of explicit coordinate dependence in the Lagrangian does not strongly hinder the existence of stable solutions compared to the impurity-free scenario. We find Bogomol'nyi equations that give rise to global minima of the energy and present some BPS configurations.
Article
Materials Science, Multidisciplinary
Jiawei Li, Yanpeng Zhang, Jianhua Zeng
Summary: Optical lattices and Feshbach resonance management are powerful techniques for studying Bose-Einstein condensates. This study combines these techniques to investigate the formation and dynamics of 3D nonlinear localized gap modes, providing important insights into soliton physics in multidimensional space.
ADVANCED PHOTONICS RESEARCH
(2022)
Article
Physics, Particles & Fields
D. Bazeia, M. A. Marques, M. Paganelly
Summary: This work investigates electrically charged structures localized in two and three spatial dimensions. The Maxwell-scalar Lagrangian is used to describe different systems with distinct interactions for scalar fields. The approach relies on finding first order differential equations that solve the equations of motion and ensure stability of the corresponding minimum energy solutions. The paper illustrates the various possibilities in two and three spatial dimensions, examining different examples of electrically charged solutions that have internal structure.
EUROPEAN PHYSICAL JOURNAL C
(2022)
Article
Physics, Particles & Fields
D. Bazeia, A. S. Lobao Jr
Summary: We investigate braneworld models with multiple scalar fields and generalized dynamics. The inclusion of cuscuton dynamics, using a new mechanism to control the internal structure of the brane in modified gravity, induces significant changes in the profile of the brane.
EUROPEAN PHYSICAL JOURNAL C
(2022)
Article
Physics, Particles & Fields
D. Bazeia, A. S. Lobao Jr
Summary: In this work, we investigate braneworlds generated by multiple scalar fields. The study focuses on the necessary formalism to examine models and evaluate the stability conditions of the gravitational sector under linear perturbations. Specifically, we develop a mechanism to explore distinct scenarios controlled by two and three fields, with a particular emphasis on how these fields can be utilized to modify the internal structure of the brane.
EUROPEAN PHYSICAL JOURNAL C
(2022)
