Article
Physics, Multidisciplinary
Yongping Zhang, Zhu Chen, Biao Wu, Thomas Busch, Vladimir V. Konotop
Summary: The interaction between nonlinearity and PT symmetry in a periodic potential results in peculiar features of nonlinear periodic solutions, including thresholdless symmetry breaking and asymmetric (multi-)loop structures of the nonlinear Bloch spectrum. These features are explained within the framework of a two-mode approximation and an effective potential theory and are validated numerically.
PHYSICAL REVIEW LETTERS
(2021)
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
Physics, Multidisciplinary
S. Wang, Y. H. Liu, T. F. Xu
Summary: In this study, we numerically investigate the properties of gap solitons in Bose-Einstein condensates with spin-orbit coupling in a parity-time symmetric periodic potential. The depths and periods of the imaginary lattice are found to have a significant influence on the shape and stability of the solitons, while the different periods of the imaginary part have little effect on the stability.
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
Optics
Yingying Zhang, Yali Qin, Huan Zheng, Hongliang Ren
Summary: This study investigates the propagation properties of out-of-phase dipole solitons and single-charged vortex solitons in a periodic photonic moire lattice. The peculiar energy band structures and extensive bandgaps of the lattice contribute to the realization and stability of the solitons. The evolution and phase variation of the solitons exhibit distinct characteristics depending on their types.
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
Optics
Peijun Chen, Hong Wang
Summary: This article investigates the dynamics and stability of two-dimensional vortex dipole solitons in nonlocal nonlinearity with a PT-symmetric Scarff-II potential. The solitons with single charge and higher-order charge are analyzed using analytical and numerical methods. It is found that the degree of nonlocality affects the evolution of the beams. The vortex dipole solitons undergo stable deformation rather than maintaining their basic profile when the nonlocality is strong. Additionally, the stability of the vortex dipole solitons depends on the potential depth, and there exists a threshold below which the beams can keep their shapes and propagate stably regardless of the strength of nonlocality. Numerical simulations support the analytical results.
Article
Optics
Weizhao Cheng, Weijie Liu, Quancheng Liu, Feng Chen
Summary: In this study, the experimental observation of the topological Anderson phase in one-dimensional quasi-periodical waveguide arrays produced by femtosecond laser writing is reported. The researchers dynamically tuned the interdimer hopping amplitudes of the waveguide array to generate the quasi-periodic disorder of the coupling constants for the model. The experimental results are consistent with theoretical simulations, confirming the existence of the disorder-driven topological phase in the photonic lattice.
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
Mathematics, Interdisciplinary Applications
Chunyan Li, Vladimir V. Konotop, Boris A. Malomed, Yaroslav V. Kartashov
Summary: This study reveals the mechanism of linear and nonlinear localization induced by spatially periodic modulation of spin-orbit coupling. It shows that specific chemical potential can lead to localized solitons or vortex solitons, and their stability strongly depends on the potential's location in the gaps.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Acoustics
I. Ioannou Sougleridis, O. Richoux, V. Achilleos, G. Theocharis, C. Desjouy, D. J. Frantzeskakis
Summary: This study investigates the propagation of high-amplitude sound waves in an air-filled acoustic waveguide. The research finds that nonlinear losses play a crucial role in the dynamics of the high amplitude pulses, and proposes a numerical scheme that captures the experimental results well.
JOURNAL OF SOUND AND VIBRATION
(2023)
Article
Automation & Control Systems
Yashan Xu
Summary: A new method for describing periodic stabilization is proposed in this study, analyzing it through detectability inequality.
SYSTEMS & CONTROL LETTERS
(2021)
Article
Optics
Pengfei Li, Boris A. Malomed, Dumitru Mihalache
Summary: The study investigates symmetry-breaking and restoring bifurcations of solitons in a fractional Schrodinger equation, especially in the presence of CQ nonlinearity and a parity-time-symmetric potential. Solitons destabilize at the bifurcation point, but stability is restored through an inverse bifurcation in the case of CQ nonlinearity. Two mutually conjugate branches of ghost states are created in the presence of fractional diffraction.
Article
Mathematics, Applied
Zhenguo Wang, Yuanxian Hui, Liuyong Pang
Summary: In this paper, we consider the existence of gap solitons for a class of difference equations under general asymptotically linear conditions on the nonlinearity, and establish the results using variational methods allowing the nonlinearity to be sign-changing.
Article
Optics
Y. Cao, T. F. Xu
Summary: We studied gap solitons and nonlinear Bloch waves in Kerr nonlinear systems under competition between quadratic and quartic dispersions. The results show that nonlinear Bloch waves can still be regarded as infinite fundamental gap solitons chains. We also revealed the properties of the gap solitons in the relevant band gaps by numerical analysis.
