Article
Optics
Khaled A. Gepreel, Elsayed M. E. Zayed, Mohamed E. M. Alngar, Anjan Biswas, Padmaja Guggilla, Salam Khan, Yakup Yildirim, Abdullah K. Alzahrani, Milivoj R. Belic
Summary: This paper explores soliton solutions to the nonlinear Schrodinger equation with Kudryashov's arbitrary form of refractive index and two forms of nonlocal nonlinear forms, obtaining a complete spectrum of soliton solutions through modified Kudryashov's method and an addendum. The criteria for the existence of such solitons are also outlined.
Article
Multidisciplinary Sciences
N. Moroney, L. Del Bino, S. Zhang, M. T. M. Woodley, L. Hill, T. Wildi, V. J. Wittwer, T. Sudmeyer, G-L Oppo, M. R. Vanner, V Brasch, T. Herr, P. Del'Haye
Summary: The authors demonstrate an all-optical method to control the polarization of light using the Kerr nonlinearity in an optical resonator. They show that the Kerr effect can be utilized to control the polarization of continuous wave lasers in a high-finesse Fabry-Perot resonator. This research has implications for polarization control in photonic circuits and the development of polarization filters and sensors.
NATURE COMMUNICATIONS
(2022)
Article
Physics, Multidisciplinary
S. S. Gopalakrishnan, K. Panajotov, M. Taki, M. Tlidi
Summary: Stable dissipative light bullets are found in Kerr cavities, forming isolated structures or clusters. The number and distribution of light bullets are determined by initial conditions, with constant peak power. Increasing beam strength leads to unstable light bullets and the formation of giant, short-lived pulses, with statistical characteristics revealing extreme events known as rogue waves.
PHYSICAL REVIEW LETTERS
(2021)
Article
Multidisciplinary Sciences
Miles H. Anderson, Wenle Weng, Grigory Lihachev, Alexey Tikan, Junqiu Liu, Tobias J. Kippenberg
Summary: Researchers have discovered a new type of dissipative structure called "zero-dispersion solitons" which combine switching waves and dissipative solitons. These structures can exist in the regime where group velocity dispersion approaches zero and have stable solitary structures. They have the potential for generating wideband frequency comb spectra.
NATURE COMMUNICATIONS
(2022)
Article
Engineering, Electrical & Electronic
Ghazala Akram, Maasoomah Sadaf, Fizza Sameen
Summary: This article discusses the application of the complex Ginzburg-Landau equation in nonlinear fiber optics and explores its solutions using the generalized projective Riccati equations technique. Various soliton solutions are extracted and their solitonic behavior is examined through graphical illustrations.
OPTICAL AND QUANTUM ELECTRONICS
(2022)
Article
Optics
Pierce c. Qureshi, Vincent Ng, Farhan Azeem, Luke s. Trainor, Harald g. Schwefel, Stephane Coen, Miro Erkintalo, Stuart g. Murdoch
Summary: Optical microresonators provide a promising platform for generating optical frequency combs. By driving two optical combs with optical pumps of different azimuthal mode numbers, the parameters of the radio-frequency comb spectrum can be discretely fine-tuned.
Article
Optics
Pierce C. Qureshi, Farhan Azeem, Luke S. Trainor, Harald G. Schwefel, Stephane Coen, Miro Erkintalo, Stuart G. Murdoch
Summary: Optical microresonators are used to generate optical frequency combs, and the parameters of the radio-frequency comb spectrum can be finely-tuned by interfering two optical pumps with different azimuthal mode numbers. Experimental results show that a discrete tunability of about 1MHz in the line-spacing of the radio-frequency comb can be achieved.
Article
Optics
Syed Tahir Raza Rizvi, Sarfraz Ahmad, M. Faisal Nadeem, Muhammad Awais
Summary: In this paper, optical solitons and other solitary wave solutions for (2+1)-dimensional nonlinear Schrodinger equation (NLSE) are obtained using extended modified auxiliary equation mapping method with cubic-quintic-septic nonlinearity. Bright, dark, singular, rational, periodic and many other solitary wave solutions are obtained for the governing model with constraint conditions.
Article
Mathematics, Interdisciplinary Applications
M. Tlidi, S. S. Gopalakrishnan, M. Taki, K. Panajotov
Summary: The study reveals the presence of stable light bullets and clusters in the monostable regime, as well as the occurrence of three-dimensional dissipative structures in a strongly nonlinear regime with subcritical modulational instability. It highlights the formation of optical 3D crystals in both super-and sub-critical modulational instability regimes, with body-centered-cubic (bcc) crystals predicted to be the most predominant. Numerical simulations confirm the robustness of bcc crystals compared to other self-organized structures. Additionally, the formation of light bullets and clusters in a bistable regime is demonstrated.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Multidisciplinary Sciences
Gang Xu, Alexander U. Nielsen, Bruno Garbin, Lewis Hill, Gian-Luca Oppo, Julien Fatome, Stuart G. Murdoch, Stephane Coen, Miro Erkintalo
Summary: Researchers observed spontaneous symmetry breaking of dissipative optical solitons in a nonlinear optical ring resonator, leading to the coexistence of distinct vectorial solitons with asymmetric polarization states. By perturbing the system, deterministic switching between the two symmetry-broken dissipative soliton states can be achieved. This work provides fundamental insights into multi-mode nonlinear optical resonators, dissipative structures, and spontaneous symmetry breaking in coherently driven Kerr resonators.
NATURE COMMUNICATIONS
(2021)
Article
Optics
Xue Dong, Zhiqiang Wang, William H. Renninger
Summary: In this study, we address the limitations of fiber Kerr resonators in generating longer pulses and complicated techniques for single-pulse generation. By demonstrating fiber Kerr resonators based on stretched-pulse solitons, we achieve robust single-pulse performance with 120-fs pulse durations. The performance of stretched-pulse solitons strongly depends on the total cavity length, and an optimized length is found to be crucial for achieving stable stretched-pulse solitons.
Article
Optics
Xiaoxiao Xue, Philippe Grelu, Bofan Yang, Mian Wang, Shangyuan Li, Xiaoping Zheng, Bingkun Zhou
Summary: This article investigates a novel class of solitons that are generated in spectrally confined optical cavities with practically no dispersion, leading to the generation of stable dispersion-less dissipative solitons. The interplay between the Kerr nonlinearity and spectral filtering results in Nyquist-pulse-like solitons with ultra-flat spectra, and the transition from soliton molecules to single solitons is also observed.
LIGHT-SCIENCE & APPLICATIONS
(2023)
Article
Physics, Multidisciplinary
Aleksandr Tusnin, Alexey Tikan, Kenichi Komagata, Tobias J. Kippenberg
Summary: This paper investigates the application of dissipative Kerr solitons (DKS) based microresonator frequency combs in coupled resonator systems. A model for a one-dimensional lattice of microresonators is derived, and two different dynamical regimes, elliptic and hyperbolic, are identified. Turing patterns, regularized wave collapse, and 2D DKS are studied in these regimes. The study also extends the system to the Su-Schrieffer-Heeger model, showing the dynamics of edge states and edge-bulk interactions initiated by edge-state DKS.
COMMUNICATIONS PHYSICS
(2023)
Article
Multidisciplinary Sciences
Bok Young Kim, Jae K. Jang, Yoshitomo Okawachi, Xingchen Ji, Michal Lipson, Alexander L. Gaeta
Summary: In this study, all-optical synchronization of Kerr combs is demonstrated in the nonsolitonic, normal GVD regime, generating phase-locked combs with high pump-to-comb conversion efficiencies and relatively flat spectral profiles. The results reveal the universality of Kerr comb synchronization and suggest a promising path towards coherently combined normal GVD Kerr combs with spectrally flat profiles and high comb-line powers in an efficient microresonator platform.
Article
Optics
Thomas Bunel, Matteo Conforti, Zoheir Ziani, Julien Lumeau, Antonin Moreau, Arnaud Fernandez, Olivier Llopis, Julien Roul, Auro M. Perego, Kenneth K. Y. Wong, Arnaud Mussot
Summary: We observed a Kerr frequency comb induced by modulation instability in an all fiber Fabry-Perot resonator. The frequency comb was fully characterized using a commercial 10 MHz resolution heterodyne detection system, revealing more than 125 comb teeth within each of the modulation instability sidelobes. We also discovered the fine temporal structure in phase and intensity of the output Turing patterns. The experimental results generally agree with numerical simulations.
Article
Mathematics, Applied
Hao Liu, Yuzhe Li
Summary: This paper investigates the finite-time stealthy covert attack on reference tracking systems with unknown-but-bounded noises. It proposes a novel finite-time covert attack method that can steer the system state into a target set within a finite time interval while being undetectable.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sofia F. Lavrova
Summary: The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Qiang Ma, Jianxin Lv, Lin Bi
Summary: This paper introduces a linear stability equation based on the Boltzmann equation and establishes the relationship between small perturbations and macroscopic variables. The numerical solutions of the linear stability equations based on the Boltzmann equation and the Navier-Stokes equations are the same under the continuum assumption, providing a theoretical foundation for stability research.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
S. Kumar, H. Roy, A. Mitra, K. Ganguly
Summary: This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Isaac A. Garcia, Susanna Maza
Summary: This paper analyzes the role of non-autonomous inverse Jacobi multipliers in the problem of nonexistence, existence, localization, and hyperbolic nature of periodic orbits of planar vector fields. It extends and generalizes previous results that focused only on the autonomous or periodic case, providing novel applications of inverse Jacobi multipliers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)